A quick introduction guide to upgrading armor.

There are 2 types of armor. You can have Full Sets, which is one piece that uses up helm/torso/leg as one, or you can have individual pieces. I will be blunt with this. Full sets, statwise, are inferior to individual armor pieces. Will go more into this later.

Armor pieces have 4 stats, 1 trait, and 1 load effect.
Stats are Physical and Magic Defense and Evasion.
Traits add different stats, like 1 Str, or 10 Mobility.
Load effect is really true or false. True you get an extra 5 ability load. False you don't.

So for min-maxing, you want ideally decent stats, the traits you want, and load. Honestly that's all there is to it. Onto upgrading!

Like armor types, there are two types of upgrades.
Stat upgrades impact Physical and Magic Defense and Evasion. Trait upgrades add a new trait onto your armor!

Stat upgrades have a capped limit of how much they can go up to. For example, Hero Armor Chestplate starts at 11 Physical Evasion, and caps at 15. However, Swimsuit, which is a full set armor, starts at 15 and goes to 30.
This means that full sets already can falter behind by having a lower stat cap. While it can have up to 2x the stats of one piece of armor, you're comparing it to 3 pieces.

Trait upgrades are different than Stat upgrades. Atmaliths and Magicites from Eidolons grant a different use when upgrading equipment. They affix a second special stat on it. For example, say an armor starts with 2 Strength. You toss on a Goblin Atmalith, and it'll add 20 Max AP as well. However, each armor piece is capped at one additional Trait. Again, this means that full sets get the shaft in that while you can add an additional three traits to individual armor pieces, you can only add one to a full set.
However, some trait upgrades can stack on a single armor. So adding two Goblin Atmaliths will grant 40 Max AP. They will continue to stack until the game will literally tell you "This upgrade has reached the limit". This varies from trait to trait though.

Upgrading tl;dr.
For min max, be sure to try and pick individual armor pieces with 5 load.
Each armor piece can recieve a certain amount of stat upgrades, they have a cap.
Each armor piece can be upgraded with one additional trait type.