BrightAmethyst seems to have answered most of them pretty well, but I'll add a bit about housing.

Having access to some form of housing, whether that's an apartment, a personal house, or an FC house, gives you access to a chocobo stable, which helps with training your feathered companion and lets you adjust the color of his plumage.

Any housing, even an apartment, allows for at least a limited version of gardening using flowerpots, but some seeds can only be acquired by crossbreeding different plants, which can only be done in an outdoor garden of a house. (Apartments don't have a place for a full garden, just flowerpots.)

FC houses can also have a workshop. (Personal houses cannot, though. It's strictly an FC thing.) A workshop lets crafters in your FC build airships and submersibles to send out on voyages to collect stuff, or build special house exteriors, or a few other projects.

Houses can have furnishings that offer a boost, like crafting stations that boost your CP (crafting points), or food items that boost any of a variety of combat stats.

NPC vendors can be stationed at your house or apartment. Though they don't offer anything that isn't available elsewhere, they do provide some added convenience in offering items in one place that you'd otherwise have to travel around to different NPCs in different areas to get (at least when the market board doesn't have them at a good price).

Unless I'm forgetting something, I think that's all the housing benefits apart from the obvious having a place to decorate and call your own.