For armor your character will only be able to unlock appearances from the primary armor type. Because leather is the primary armor type for Monks, you can only unlock appearances for leather items on your monk.
The game currently lets players equip all armor types equal to or lighter than their primary armor type. Plate wearers can wear everything because they have the heaviest armor, while cloth wearers can only wear cloth. The armors are ranked as such: Cloth < Leather < Mail < Plate. There is a balance argument here in that if players could unlock appearances for everything they can equip everyone would just farm with a plate wearer and get all of the armor unlocks while cloth wearers wouldn't be able to.
Additionally for weapons you will of course only unlock the appearance of items you can equip.
Source: Here is a WowHead article that extensively covers the ins and outs of the system
Q - What about things we can't equip?
A - Short answer, No. Long answer, essentially let's say you play a Death Knight. If a quest reward offers you a shield, or you loot a shield, that shield will not be added to your wardrobe. If you cannot equip the item, it will not be added. That being said, even if a Death Knight can equip a cloth helm, it still will not be added to your wardrobe because it is not meant for your class, at the same time, the if you got Class:Warrior tier, it still won't count. So to clarify, you must be able to equip the item, it must be of your primary armor type, and it must be able to be obtainable and equipped by your class. Once these terms are met, then the item will be added to your wardrobe.
Although not a direct answer this blue post from beta forums talks about how the system specifically focuses around appearances a character can actually transmog.
Our primary goal for appearances is to ensure that all appearances that a character can currently use as a transmog source in Warlords of Draenor will continue to use that transmog source in Legion. We know of a few Beta issues that violate this rule (racial restrictions, armor type changes), and we’re working through them. However, we will probably have a few appearances that are still missing (examples: low-level mail/leather conversions). Don’t panic! Let us know what we missed, and we’ll address them as soon as we can.