If your circumstances don't allow a more traditional pet...

Consider the humble, friendly, and personable domestic rat! From OregonLive.com, "Kissy, squishy, beautiful rats at the rat fanciers' show in Hillsboro."

Side note: I really dig that they have categories in the rat show like kissiest and squishiest. I think dog shows would probably be more interesting to the general public if those categories were added, although I understand not wanting to compromise the serious nature of many of those events.