We don't really care about low rank gear. There's some staple skills found here or there, but the one Skill we really want on every set, Rapid Morph, is extremely limited this early on.
Most of the recommendations until RMRapid Morph becomes more accessible are optional, in case you don't want to be naked.
It’s a slightly different story for the Weapon choice, as there’s two options that can get you all the way into endgame that open up pretty much right out of the gate:

Weapon	Material	Where to Get it
Proto Iron Axe I (Ore Tree)	3x Iron Ore*	Shrine Ruins, Blue Ore*
Proto Iron Axe II (Ore Tree)	2x Icium	Frost Islands, Mining Ore
	1x Earth Crystal	Shrine Ruins, Mining Ore
	2x Iron Ore	Shrine Ruins, Blue Ore
*Proto Iron Axe I can also be bought for 600z.

If you don’t see the option to upgrade or craft yet, keep progressing, this list just helps identifying the earliest point in time you can obtain the material.
As for armor pieces, nothing is particularly great, as to be expected this early into the game. If you feel uncomfortable going naked, consider making the following pieces:
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heres where text describing the set goes
Remember: If you don't see a monster mentioned here in your Quest List yet, just keep progressing. You can't miss anything, so don't worry about progressing too far or not completing every quest.

Piece	Material	Where to get it
Izuchi Helm	1x Monster Bone S	Gather any low rankAll of Kamura, 1-3* in the Gathering Hub Bonepile, hunting Great Izuchi can reward them too
	2x Great Izuchi Pelt	Hunt Great Izuchi, the droprate for Pelts is very high
	1x Izuchi Pelt	Hunt (non-Great) Izuchi, you have a high chance of carving their Pelt
Izuchi Mail	2x Great Izuchi Hide	Hunt Great Izuchi, look out for shiniessparkling objects on the ground, as they have a very high chance of being Hide
	2x Great Izuchi Pelt	Hunt Great Izuchi, the droprate for Pelts is very high
	1x Sharp Claw	Hunt and Carve (small) Izuchi and Jagras. Their Quests have an acceptable droprate and you can sometimes carve them directly. You don't need that many, luckily
Izuchi Coil	2x Great Izuchi Pelt	Hunt Great Izuchi, the droprate for Pelts is very high
	1x Sharp Claw	Hunt Izuchi and Jagras, do their quests too
	1x Izuchi Pelt	Hunt (non-Great) Izuchi, you have a high chance of carving their Pelt
Lagombi Greaves	2x Twisted Remains	Gather Bonepiles in Shrine Ruins
	2x Lagombi Plastron	Hunt Lagombi, the Plastron has a very high chance to be rewarded from carves and just hunting it in general
	2x Lagombi Pelt	Hunt Lagombi and Carve it, look out for shiniessparkling objects on the ground too
Hub 1*/Village 1-2* Set: Item List

Weapon	Material	Where to Get it
Improved Steel Axe	3x Dragonite Ore	Lava Caverns, mine Ore
	2x Monster Bone L	Low Rank: Hunt Pukei-Pukei or Rathian or Somnacanth
The last combined upgrade for this weapon, from here, two main options open up. It’s up to preference which upgrade path you follow, both will be listed here.

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It is now that we get access to our most important skill: Rapid Morph. Unfortunately, you won’t be able to max it out quite yet, but it’s a start.
RMRapid Morph improves the speed and damage of our Morphs, which is the majority of the moves we want to use anyway.

Piece	Material	Where to get it
Volvidon Mail	1x Great Izuchi Hide	Hunt Great Izuchi, look out for shiniessparkling objects on the ground, as they have a very high chance of being Hide
	2x Dragonite Ore	Lava Caverns, mine Ore
	2x Volvidon Claw	Hunt Volvidon. CapturingHunt normally until a blue icon shows up on the top right, put down a trap and throw 2 Tranqbombs at it it increases your chances, but they're not terribly rare
	2x Volvidon Shell	Hunt Volvidon, you can break its Back for an extra chance for one but overall the Shell is common
Volvidon Coil	2x Warm Pelt	45% Chance to carve from Kelbi
	2x Jumbo Bone	Hunt Arzuros, Lagombi or Volvidon, they're a little rarer but still easy enough to come by. Popo can also reward them
	2x Volvidon Rickrack	Break Volvidon's Back for a 70% chance to get one. You can also carve them and get them from quest rewards themselves at a lower chance
	2x Paralysis Sac	More Volvidon, 40% chance to carve the Paralysis Sacs from it
Hub 2*/Village 3-4* Set: Item List

The end of Low Rank (LR), alongside split upgrade paths.
Exhaust Phials can KO monsters by hitting their face repeatedly and amp faster.
Power Phials are stronger but amp slower. This one also has an element to take into consideration. The amp generation will be a non-factor after a certain point in progression.

Weapon	Material	Where to Get it
Option 1: The Shredder I (Thunder Tree)	2x Zinogre Shocker	Hunt Zinogre. Break the back for a 70% chance to get the Shocker
	3x Dragonite Ore	Lava Caverns, mine Ore
	2x Firestone	Lava Caverns, mine Ore
	1x Electro Sac	Hunt and Carve Khezu. Tobi Kadachi can reward them too, but carves are typically easier to get
The Shredder II (upgrades from Shredder I)	2x Diablos Shell	Hunt and carve Diablos, pretty common carve
	3x Fulgurbug	Hunt Zinogre of any difficulty. Supposedly they're somewhat rare as they can neither be carved nor rewarded for Part Breaks.
Option 2: Elite Switch Axe I* (Ore Tree)	1x Commendation	6* Village: Magnamalo + Zinogre Tobi Kadachi + Mizutsune Rathalos + Tigrex 3* Hub: Bishaten + Almudron Tigrex + Goss Barroth + Tobi Kadachi + Magnamalo
	2x Firestone	Lava Caverns, mine Ore
*You can skip this upgrade and craft the next weapon from scratch in High Rank.

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Armor-wise, at Village 6* / Hub 3* Almudron is unlocked and our first really nice source of Rapid Morph and thus, a set upgrade. This is a Helmet you should get used to, as it's upgrades in HRHigh Rank, Hub Quests 4-8* and in MRMaster Rank, anything in Sunbreak Hub will be recurring.
The Almudron Hands are great too, but require a Plate to craft. Generally speaking, Plates are rare items with low (1-3%) droprates, and as such i try to avoid requiring them for Progression Sets as much as possible. No point keeping you locked in any place longer than you need to be.

Piece	Material	Where to get it
Almudron Helm	1x Almudron Shell	Hunt and Carve Almudron, pretty common Item
	2x Lightcrystal	Flooded Forest, mine Ore
	3x Almudron Scale	Hunt and carve Almudron, alongside Shells, Scales are very common
	1x Almudron Whisker	Break Almudron's Head for a 80% Chance to get the Whisker
New Armor Piece

With Village (or Hub 1*-3*) done, you’ll progress into HRHigh Rank, which is Hub only.

The armors available here are nothing too great, can skip if you want. If you feel extremely lacking in defense, Izuchi is an option. If you’re a particular enjoyer of Evade Extender 1, Wroggi feet are usable for that.
As for Weapon upgrades:

Weapon	Material	Where to Get it
The Power Shredder (Thunder Tree)	5x Fucium	HRHigh Rank, Hub 4*+ Flooded Forest, Sandy Plains, Lava Caverns, Mining
	3x Thunder Sac	Same as in LRLow Rank, Hub 1-3*, All of Village, Hunt and Carve HRHigh Rank, Hub 4*+ Khezus, the Sacs are common enough from them
	2x Pearl Hide	Hunt HRHigh Rank, Hub 4*+, breaking the Legs guarantees at least one Hide
General's Strongaxe I* (Ore Tree 2)	2x Gracium	(HR) Frost Islands, the White Ore specifically
	2x Twisted Rockbone	Gather Bone Piles in Shrine Ruins (HR)
	3x Dragonite Ore	Lava Caverns, mine Ore
*You can also craft this weapon from scratch instead, the 2x Golden Muck can be obtained from Low Rank Almudron and the 3x Quality Bones are from High Rank Bonepiles.

With this, the Power Shredder is at its highest upgrade until you progress into Master Rank.

A new rank, a new upgrade:

Weapon	Material	Where to Get it
General's Strongaxe II (Ore Tree 2)	2x Novacrystal	(HR) Frost Islands, the White Ore specifically
	4x Basarios Carapace	Hunt High Rank Basarios, break the head for a 70% Chance to get one. Carapace is a common carve aswell
	4x Monster Keenbone	Can drop as a reward from any of the following (high rank) hunts: Jyuratodus, Rathian, Barroth, Khezu, Pukei-Pukei, Aknosom. Slightly rarer drop as it again can't come from carves or partbreaks

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Armor-wise, Volvidon makes a comeback. Do note that the feet have Evade Extender 2, which can seriously throw off your positioning but is great for getting around. If you decide against them, use the Low Rank Almudron Helmet, the rest of the pieces are not overly important (yet). Slot Gear Skills Head Almudron OR whatever Rapid Morph 1 Chest Volvidon S Rapid Morph 1 Hands Anything Goes Waist Volvidon S Rapid Morph 1 Feet Volvidon S* Rapid Morph 1, Evade Extender 2 As before in LR, you’ll want to use any 3 of those 4 pieces.

Piece	Material	Where to get it
Volvidon Mail S	1x Great Izuchi Hide	Target Reward: 21% Capture Reward: 26% Broken Part Reward: 20% (Tail) Carve Reward: 43% (Body) Dropped Material Reward: 30%, 60%
	2x Dragonite Ore	Lava Caverns, mine Ore
	2x Volvidon Claw	Target Reward: 19% Capture Reward: 34% Carve Reward: 19% (Body) Dropped Material Reward: 15%, 20%
	2x Volvidon Shell	Target Reward: 15% Capture Reward: 26% Broken Part Reward: 30% (Back) Carve Reward: 40% (Body) Dropped Material Reward: 35%, 55%
Volvidon Coil S	2x Warm Pelt	45% Chance to carve from Kelbi
	2x Jumbo Bone	Arzuros (16%) Lagombi ImageLagombi (16%) Bishaten ImageBishaten (14%) Volvidon ImageVolvidon (13% (x2)) Tetranadon ImageTetranadon (12%) Popo Image
	2x Volvidon Rickrack	Target Reward: 22% Broken Part Reward: 70% (Back) Carve Reward: 24% (Body)
	2x Paralysis Sac	Target Reward: 15% Capture Reward: 26% Broken Part Reward: 30% (Back) Carve Reward: 40% (Body) Dropped Material Reward: 35%, 55%
New Armor Pieces

Make the Zinogre Chestpiece, the Anjanath Coil and the Remobra Feet. You’re 1 Rank away from your set finally coming together. Use the same pieces you used until now. Nothing noteworthy here otherwise, so just move on. Also, no weapon upgrades. You can craft the Rathalos Coil S if you're luckier with his rare.:(
Alternatively, make either the Dober Coil or Baggi Coil S. Dober needs an Eroded Husk which you can gather from HR Bonepiles in Sandy Plains.

Weapon	Material	Where to Get it
Zinogre Mail S	1x Zinogre Plate	Hunt Zinogre, either Low or High Rank. Break the head Twice and cut the tail for best chances, High Rank has slightly better odds. It's the rare drop. Either grind this or go for a Talisman with Wex 1Weakness Exploit 1 or better.
	1x Zinogre Claw+	Hunt Zinogre, break the front Legs, roughly 90% chance to get at least 1
	3x Zinogre Electrofur	Hunt Zinogre, relatively common reward and carve
	3x Zinogre Carapace	Hunt Zinogre, common carve to get from them
Rathalos Braces S	3x Inferno Sac	Several Monsters can drop this, but your best chances are HR Aknosom and HR Rathalos.
	1x Rath Wingtalon+	High Rank Rathian and Rathalos, break the Wings for a good chance
	4x Rathalos Scale+	High Rank Rathalos, cut the tail, break the head and carve it for the best Chance. It's a common item on paper but somehow it's also the one Item thats historically grindy for some reason
	2x Uroktor Scale+	High Rank Uroktors, the tiny Leviathans in Lava Caverns that dig underground and shoot back up. Pretty common carve
Anjanath Waist S	2x Monster Hardbone	Capture HR Somnacanth for extra chances, most 6* Hub Quests reward those, for a list, see here (Kiranico, opens in new tab).
	4x Anjanath Pelt+	High Rank Anjanath, relatively common carve from them
	2x Anjanath Scale+	High Rank Anjanath, break the legs and Carve for a very good chance to get some.
	1x Anjanath Gem	High Rank Anjanath's Rare Drop, another grind unfortunately. Can replace with Rathalos Waist if you're feeling more lucky about his rare.
Remobra Feet S	2x Stripe Hide	Carve from Remobra (small flying wyverns), roughly 30% chance in either Low or High Rank
	1x Firecell Stone	HR Lava Caverns, mine Ore
	2x Pukei-Pukei Scale+	High Rank Pukei, 40ish% chance when carving
	1x Monster Hardbone	Capture HR Somnacanth, 14% chance to get 2, 7% from the rewards
Note: Those pieces are for the HR7+ set, they're not for use just yet.

The final HR upgrade of the exhaust phial choice is in HR7.
You'll spend most of your time unlocking and grinding for Decos here. If you have the Sunbreak DLC, feel free to make the set from MR and then come back to make it slightly faster.

Weapon	Material	Where to Get it
Conqueress (Ore Tree 2)	4x Rakna-Kadaki Carapace	Hunt Rakna-Kadaki, Carapaces are fairly common
	2x Firecell Stone	HR Lava Caverns, mine Ore
	2x Gold Rajang Pelt	Somewhat rare Rajang drop, it's about 10% per carve
	4x Great Stoutbone	Rajang - 10% chance from the rewards only. Somewhat rare as a result, but still doable

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This is a low-budget, RNG-FreeWhen MH people talk about RNG, it typically refers to stuff you cannot target-grind, like Decos in World or Talismans in every other MH. progression set. If you don't have Sunbreak, or want to challenge yourself first, you can also try to get the full Valstrax Set, either at HR 100 or through his Event Quest. That set, with appropriate Decorations, will be good enough to skip every single MR set until Postgame-Progression (MR10+).

Additionally, you now have access to most of the decorations, including some important ones.
It's heavily recommended to craft the important ones now, or immediatly after you made your first MR set, assuming you have the Sunbreak DLC.
The following Decorations will be relevant throughout the remainder of Base Rise, aswell as all of Sunbreak and just make Setbuilding so much easier.
This guide assumes that you have the following decos in Master Rank:

Total mat requirements

Deco Skill (DecoName)	MaterialComplete! Material list, not per deco	Where to Get it
3x Speed Sharpen 1 (Grinder Jewel 1)	3x Great Izuchi Tail+	HR Great Izuchi, break the tail, 80%
	6x Rath Wingtalon+	High Rank Rathian and Rathalos, break the wings for a very high chance to get the Wingtalons
	6x Aquaglow Jewel	Most quests in Hub 4*-6* (chances are you just have enough from progressing)
3x Weakness Exploit 1 (Tenderizer 2)	3x Narga Medulla	Hunt Nargacuga, Cut the tail. 12% Chance from the tailcarve, 7% from the Body Carve, 5% as quest reward
	9x Rakna-Kadaki Spike	Rakna-Kadaki, break the legs (not the Webbings, the actual Legs) and the Glowgut (yellow butt), then capture it
	9x Almudron Claw+	HR Almudron, 90% chance when breaking the forelegs
	15x Lazurite Jewel	Welcome to the actual Pain Point of this. These drop from 7* Hub Quests, mostly from the Apexes. Arzuros and Rathian probably die the fastest, but any of them are fine choices
1x Attack Boost 1 (Attack 2)	1x Magnamalo Plate	Like any other Plate, you can farm this either in Low Rank1% Shiny 1% Carve 3% Break Head 3% Capture Reward 2% Quest Reward for quicker kills but lower chances, or in High Rank.
	3x Goss Harag Claw+	80% Chance when you break the Arms, actual arms, not just the Ice
	3x Rajang Blackfur	Common Carve from Rajang
	5x Bloodrun Jewel	Most hub 6* and 7* Quests reward them
1x Rapid Morph 1 (Quickswitch 2)	1x Somnacanth Claw+	HR Somnacanth, break the arms for 80% Chance, then capture
	2x Rakna-Kadaki Silk	Rakna-Kadaki, break the legs
	2x Tigrex Claw+	HR Tigrex, 80% Chance when you break the claws
	3x Bloodrun Jewel	Same as for the ABAttack Boost Deco above, most 6* and 7* Hub Quests reward these

Additionally, the MRMaster Rank portion of this guide assumes you obtain the following Decorations, which will be the last Deco Grind until the Post-Game Progression:

Decoration	Material	Where to Get it
3x Critical Boost (Critical 2)	3x Almudron Plate	Almudron's Rare; Same deal as before, Low Rank has lower chances but is faster, High Rank has higher chances. Make sure to cut and carve the tail and break the head
	6x Magnamalo Horn+	HR Magnamalo, 92% for Headbreak, 25% for Capture
	15x Lazurite Jewel	7* Hub quests (Apexes, Advanced etc)
	6x Apex Blaze Sac	Apex Rathalos, 8% from Quest Rewards, 12% from Carves, 35% from breaking the Head.
2x handi deco	2x Purple Magna Orb	High Rank Magnamalo Rare, cut the tail and break the Head, it's a toss up between capturing and killing. Good luck.
	16x Lazurite Jewel	7* Hub quests (Apexes, Advanced etc)
	12x Daora Dragon Scale+	Somewhat common reward for hunting Kushala Daora. Kush unlocks at HR30, so feel free to come back to this after making your first MR set
	6x Daora Horn+	80% Chance when breaking the Head (can't break above 35% health), 17% from carving
1x Protective Polish (Sharp 2)	1x Great Izuchi Tail+	HR Great Izuchi, 80% when breaking the Tail
	3x Narga Razor	HR Nargacuga, break the wingblades and you're guaranteed to get at least one
	4x Magnamalo Blade+	HR Magnamalo, 80% chance when breaking the Arms
	4x Lazurite Jewel	7* Hub quests (Apexes, Advanced etc)

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This guide will assume decorations and a charm of at least 2 level 2 slots from here on. Skills on the charm can replace decorations that would otherwise occupy level 2 slots, otherwise treat them as bonus.
MR1 gives us access to the Barroth Hands and Chest, as well as the Hermitaur Waist. MR2 brings the Blood Orange Bishaten, and with it, the Orangaten Greaves. Finally, in MR3, Almudron Helmet gets replaced with it's MR equivalent.
Putting all these together results in the set pictured.

In terms of Weapons, it's ultimately preference between Conqueress and Shredder. Shredder is easier to manage in solo, Conqueress might yield better results in multiplayer due to its faster amp. Shredder will however be undisputably better by late MR4. In MR1, both weapons can be upgraded:

Weapon	Material	Where to Get it
Option 1: The Powershredder+ (Thunder Tree)	3x Sapphiron Ore	Jungle, mine Ore
	5x Eltalite Ore	Mine Ore in MR, any map
	1x Awegite	MR Shrine Ruins, mine Ore
Option 2: Conqueress II (Ore Tree)	2x Frocium	MR Frost Island, mine Ore
	2x Twisted Stiffbone	MR Shrine Ruins, gather Bonepiles
	3x Eltalite Ore	Mine Ore in MR, any map
Material Requirements for MR1 Weapon Upgrades

In MR3, you can upgrade weapons again:

Weapon	Material	Where to Get it
Option 1: The Lightning Shredder (Thunder Tree)	2x Monster Slogbone	Aurora Somnacanth or Shogun Ceanataur
	1x Ultimas Crystal	Mine Ore in MR, any map
Option 2: Conqueress III (Ore Tree)	1x Centuria Ore	Citadel, mine Ore
	2x Purecrystal	MR Flooded Forest, mine Ore
	4x Basarios Cortex	Basarios
	4x Monster Slogbone	Aurora Somnacanth or Shogun Ceanataur
Material Requirements for MR3 Weapon Upgrades

Progress through MR3 and 4 until you unlock the last Switch Skills, just before the second urgent quest.

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Just before the second Urgent quest, you’ll unlock the Counter, get very accustomed to it. Hunt a Magma Almudron to unlock and craft the Switcher Rampage Deco, equip it. It grants Phial Switch Boost, which boosts phial regeneration on morphs to axe, making morph loops gauge positive, boost phial effects on sword hits of morph attacks by 10%, and makes phials apply to axe hits of morph attacks.
The Gloomcloth for the Death Stench pieces can be obtained from the Meowcenaries, by sending them to sparkling bonepiles. This set (or similar) will be your baseline going into Post- and potentially Endgame.
MR5 and 6 don’t offer a whole lot to improve it, so just stick to what you have until MR10.