The Elder Scrolls Online. That's great. How are you going to organize it all? With a house? Don't be ridiculous; what you need is the new Collections feature going live in the game's next major update. A new development blog explains how the system will allow players to organize mounts, pets, and costumes through a few tabs and a handful of blood sacrifices. (Mostly the tabs.)
Items that belong in Collections will automatically be moved over when Update 6 goes live, removing any need to worry about inventory space when you need to summon a mount or don a costume. Any new items will also be tossed right in your Collections if they fit the criteria. The Collections also allow you to see vanity pets that you haven't yet obtained, thus giving you all the more reason to hunt down those elusive little critters for your collection-related purposes.