A personal inland marine policy would cover the contents in the event of a fire, theft, etc. It would not cover the building itself, but it sounds like that is covered by the association. A personal umbrella policy should cover you for liability if your homeowner's policy would not cover you...
I didn't think my first post on GJ would be about insurance, but I thought I could at least be a little helpful here.
You need what's called a "personal inland marine" policy. Per Wikipedia: "Inland marine insurance in the United States indemnifies loss to movable or specialized types of...