Armor is broken up into divisions(categories) ranging three levels for each set. Armor labeled as beginner can be worn by all jobs and typically is only for appearance's sake and can only be purchased.
For all armor (other than beginner pieces), there are alchemy recipes that can make them. The only source of armor level 38-40 and above level 50 is from alchemy recipes. It is also possible to obtain pieces of armor from certain monsters and certain quests. Level 60 armor can be obtained from using a Level 60 Max Armor Voucher.
Quest armor generally can not be traded and only obtained once. Certain monsters and quests give slotted armor which can be enhanced by filling the slot with an Onyx obtained by chance via Dice Chests.