If you can't store it in the Armoire, you can usually buy it or loot it again somehow. If it's a quest or achievement reward, you can usually get it from the Calamity Salvager and if it's something you looted you can usually buy it from the Market Board or do the relevant dungeon again.

There are very few items you can't get again, so the order to go in is first see if you can store it in your Armoire, then see if you can buy it again from the Calamity Salvager (if you can, you can destroy it).

Your other options are to store it in the armory chest, inventory, chocobo saddlebag, glamour dresser (found at an Inn) or a retainer. Retainers are like storage banks that can also sell items for you on the market board.

What I listed sounds like a lot of different storage types but it can all fill up with useless stuff over time, so deciding if you really need it right now and making yourself sure you can get it again easily can help you maintain inventory space.