Partners can only wear regular clothing, so no clothes that have to be repaired by Fleta for example. Any kind of armor and magical clothes are a no go.
As for weapons (with the exceptions of bows, xbows and guns, they can't use them anyway) they can only use one handed weapons like say a broad sword or a celtic royal hammer.
Any personalized items (like say solodrake-only item) cannot be gifted because it belongs only to you anyway. Anything given to a partner becomes exclusively theirs, so you cannot try to remove what you gifted to them no matter what (except when using a Partner Trade Unlock Potion or by right clicking the item and permanently destroying it). Either they equip it or it sits in their inventory.