Ok, so taking all the feedback and responses thus far, I modded my thing one last time. I got rid of the melee penalty from the shield and I ditched the number of armor items cap, but I kept the heavy/light distinction.
So what we got is…
Armor
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Armor Cap. 18 Max (INCLUDING base Armor).
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Heavy Armor. Makes some checks hard when equipped. A Heavy Armor (+2) item can be purchased for the cost of three Common Armor (+1) items.
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Shields. As Heavy Armor but its cheaper and confers a penalty even if only CARRIED.
The player facing rules are easy and pretty intuitive. 1 armor light. 2 armor heavy.
So heavy armor is a more efficient use of inventory slots but it comes at a significant cost (at least early on) and makes certain things hard (stealth, arcane/nature casting, swimming, etc).
Thematically, I can make this easy to suss out. Heavy armor will be stuff like steel pauldrons, breastplates, close helms, etc. I will make heavy armor a rare and expensive thing. Even found armors may need to be smithed to fit the wearer. Its a good way to spend coin.
The dm facing assumptions are a bit trickier.
On my end, I have to make gear choice interesting. Magic items which give armor likely wont give cool stealth, casting or other such bonuses - on a rare occaision, it would be a minor bonus on a light armor piece (the Robe of the Archmagi, the Thieve’s Hood, etc). So, players can choose what they want to shine with. Defensive dude or sneaky/acrobatic/magicky dude.
We’ll see how it goes.