Zenny is pretty straightforward, and material points are a new mechanic in this game.
Armor requires three things to upgrade: zenny, material points, and armor spheres. Armor, when upgraded, will have increased Defense, which can be exceedingly helpful in getting that last bit of Defense you need (particularly in High Rank since aside from upgrading armor that’s the highest the Defense gets). Armor is by far the simplest to upgrade so we’ll start with that.