The variables that are clear to me are shown in the Armor-table (PHB 145):

1. Type of armour: Light, Medium, Heavy (also limits Dex mods).


2. Cost, commonly displayed in GP.


3. Armour Class.


4. Strength prerequisite.


5. State of disadvantage on Stealth checks.


6. Weight.

A description of the armour is also necessary. Considerations of which classes have access to the armour types seems necessary. Considerations of worldbuilding implications seem optional. Considerations of the feats that grant access to armours and improve the efficiency of armours (PHB 167-168) appears necessary.

Have I missed any important variables, such as specific class feature interactions with armour?

What I'm going to do with this:

I will homebrew (a) mundane armour, replacing those listed on the PHB's armor-table, which will then later translate to (b) magic armours that have an existing type of mundane armour as their base type. While I'm most interested in mundane armour, I'm also interested in other properties. The focus here is variables to consider before the process of brewing.

I'm solely interested in variables from the RAW. I'm currently unhappy with the flavour of armours and some of the balancing. I'm not trying to homebrew how armours function as a system. So to restructure that system, I require your expertise in analysing that system and its components to keep it functioning without breaking it by not considering variables that are integral to that system.

What I'm looking for in your answers:

A variable described (in one sentence), then a brief explanation about why this variable is to be considered for home-brewing armour, followed by the next variable until the finite number of variables is exhausted.
The best answer is the one that is most comprehensive, exhaustive and correct (RAW).

This is an example of a good answer that is further improved by its comments which I paraphrase:

The material of the armour is significant because there are classes that restrict wearing specific materials and spells that affect specific materials and creatures which have abilities that affect the material.

The most important thing to consider is maximum attainable AC.

There is a clear hierarchy in the standard armor sets in the PHB. Heavy armor grants the best potential AC, while Medium and Light armor provide less but roughly equal AC, albeith with light armor requiring much higher dexterity to accomplish said maximum. Plate grants 18 AC versus 17 AC from both half plate (15+2) and studded leather (12+5).

Low level armor follows a similar pattern, albeit with medium armor performing a bit better. Chain mail provides 16, as does scale mail (14+2), while studded leather provides 15 AC(12+3) with the maximum starting dexterity of 16.

In general, no armor should allow for a higher maximum AC than the three top-tier armors of each category. An exception could be made for armor with a significant drawback, or armor only usable with a specific class feature or feat, in which case the bonus AC should be considered a part of that feature.

The reason this maximum is so important is the bounded AC of 5th edition. Getting even +1 AC is a very rare thing, and AC becomes exponentially more powerful the higher your AC already is. For example, say you have a high level Paladin, who has taken the defense fighting style, adamantine plate armor, a +3 shield, constantly uses Shield of Faith, and through whatever means (feat or 1 class level) also has access to the Shield spell. All told, they have a base AC of 24, an enhanced AC of 26, and a emergency AC of 31.

If you allowed that player to get an extra +1 AC on top of all of that, you might think, "Well, there's only a 5% chance each time they're attacked the AC will even matter, so it's not a big bonus." However, that's not how the math actually works out.

Let's say for example an balor tries to attack this paladin. At this level the paladin probably has plenty of low level spell slots to burn on this kind of thing, so we'll use 31 AC as the target. The balor has +14 to hit, which means they need to roll a 17 to hit through the shield spell. In other words, in 16 out of 20 cases, the balor does 0 damage. In the other four cases (17-20) it does normal damage (no crits due to adamantine). On average, that means the balor does 4/20 = 20% of it's attack damage per attack.

Now lets say the paladin is able to buy some fancy form of armor that grants an extra point of AC over plate. Now their AC with everything is 32, and the balor needs to roll a 18 to hit, and our formula changes to: 3/20 = 15% of it's attack damage per attack. That 5% smaller chance to be hit actually translates into 25% less damage taken overall. If they could somehow squeeze out an extra +1 AC on top of that, 2/20 = 10% attack damage, or half as much damage taken compared to when they had just 2 AC less.

Whether it is made of metal

Druids care about this aspect a lot:

Armor: Light armor, medium armor, shields (druids will not wear armor [....] made of metal) - PHB p65

Magical Effects or Special Properties

One of the major things to consider are any magical effects or special properties the item possesses. Chapter 7 of the Dungeon Master’s Guide (DMG) focuses on treasure and rewards, including magical items.

Pages 141-143 detail special properties an item may possess. Whilst this section of the book is focusing on magical items, you as the DM could rule an item has one of these special properties but is not magical. For example, a helmet may have been designed for a cloud giant, making it too large for a medium sized creature to use. Plate armour that's not properly fitted may have the painful property. A shield may have an in-built compass or sundial.

Size and Shape

Following up from that, the size and shape of a weapon or piece of armour may be something to consider. Pages 140 and 141 of the DMG state, under "Wearing or Wielding Items", that:

In most cases, a magic item that's meant to be worn can fit a creature regardless of size or build. Many magic garments are made to be easily adjustable, or the: magically adjust themselves to the wearer.

Rare exceptions exist. If the story suggests a good reason for an item to fit only creatures of a certain size or shape, you can rule that it doesn't adjust. For example, armor made by the drow might fit elves only. Dwarves might make item only useable by Dwarf-sized and dwarf-shaped characters.

When a nonhumanoid tries to wear an item, use your discretion as to whether the item functions as intended. A ring placed on a tentacle might work, but a yuan-ti with a snakelike tail instead of legs can't wear boots

Again, this is only considering magical items. A non-magical item will not will not magically adjust its size or shape (though an armour smith may be able to adjust the piece for you, for a fee). Below is a variant rule from page 144 of the Player’s Handbook which details how size may be important for armour:

Variant: Equipment Sizes

In most campaigns, you can use or wear any equipment that you find on your adventures, within the bounds of common sense. For example, a burly half-orc won't fit in a halfling's leather armour, and a gnome would be swallowed up in a cloud giant's elegant robe.

The DM can impose more realism. For example, a suit of plate armour made for one human might not fit another one without significant alterations, and a guard's uniform might be visibly ill-fitting when an adventurer tries to wear it as a disguise.

Using this variant, when adventurers find armour, clothing. and similar items that are made to be worn, they might need to visit an armour smith, tailor, leatherworker, or similar expert to make the item wearable. The cost for such work varies from 10 to 40 percent of the market price of the item. The DM can either roll 1d4 x 10 or determine the increase in cost based on the extent of the alterations required.

How It's Used

For armour, this seems fairly obvious, you wear it and gain the AC bonus. However, certain design features, told to the players when describing the armour, may warrant a special feature, as described above. For example, gauntlets with spikes on the knuckles may add +1 damage (piercing) to an unarmed strike.

A parrying dagger or sword breaker (it doesn’t actually break swords) may grant increased AC as they are used, mechanically speaking, like a shield. However, they would still have the 1d4 piercing damage a dagger does.

Roleplaying Elements

Finally, whilst not a hard-and-fast rule, you could make your items more interesting by attaching roleplay elements to them.

For example, a fun idea could be to offer the player’s a normal shield with a yellow square painted in the centre, taking inspiration from Heraldry and Abatements. Whilst the yellow square does not offer any mechanical advantages or disadvantages, in history, a person with a big yellow blotch on their shield was easily identified as a coward. This could lead to some unique roleplaying opportunities, such as people mocking the owner of the shield. Or, wearing armour bearing alliance to an enemy army, a cult of necromancers or the Thieves Guild may cause guards of a city to attack or arrest you. It could also be done in reverse, giving the player’s the weapon or armour that an ancient hero once owned, again, allowing for unique roleplaying opportunities.

Based off the question, I could not really tell if you had implicitly covered this, but have you considered the rarity of the armor?

You listed the cost (in GP), which should pretty easily determine the rarity of the armor. I am pretty sure you are considering this, but how likely are the players to just come across this armor in a normal enemy encounter or in some slightly out of the way storage room?

Is this armor one-of-a-kind, a dime-a-dozen, or somewhere in between?

$beginarray
hline
textbfRarity & textbfCharacter Level & textbfBonus & textbfValue \
hline
textCommon & text1st or higher & – & 50–100,textgp \
textUncommon & text1st or higher & – & 101–500,textgp \
textRare & text5th or higher & +1 & 501–5,000,textgp \
textVery rare & text11th or higher & +2 & 5,001–50,000,textgp \
textLegendary & text17th or higher & +3 & 50,001+,textgp \
hline
endarray
$

With all the considerations you listed, I am sure you are already determining if the armor is balanced, but balance is definitely something that it seems a lot of people overlook until it is too late and a player breaks the game with some minor detail.

I hope this helps you as you create the armor!

Which enchantments are valid on the armor.

Many magical items in the DMG call out specific types of armor that they might be found on. If you homebrew armor, you'll have to make decisions on which armor-types might be enchanted with which options.

For example, Mithral Armor requires (medium or heavy, but not hide), which is a fancy way of saying "primarily made of metal", but if your new armor type is a Medium armor made from plants, then it likely wouldn't qualify for this "enchantment", which really is more like a special material.

Another example, Demon Armor is a form of Plate armor, which means you won't be able to use the enchantment if you replace the existing armor types, unless you decide which new type(s) will be allowed to hold it.