The inn is indeed your first house. If you do the "quest" for entering it you get some base furnishing items. Houses work pretty simply, you can set various access levels for who can access your house, and place things in them. Larger houses have more storage space in the House Vault, and house vault size is directly linked to how many items you can sell on the broker.
http://eqiiforums.station.sony.com/eq2/board?board.id=homeshow
That is a cool little forum with lots of things about housing including various things you can do with furnishings and such. They even make fireplaces that look pretty damn cool in various threads.
That really only scratches the surface in a sense, but it should give you a general idea.