Also, balancing the categories isn't at all necessary, though it can be cool. One of the two characters I've got going in PBP has no prop or people Aspects at all, but he works fine. The other has all phrase Aspects, but two double as people and a third as a prop, and he also works fine.
It depends on what kind of character you want to play, whether very self-contained aside from maybe the other PCs, or very much in-tune with people and places they are.
As for story vs. situation, I wouldn't worry about it too much. Come up with a story and story Aspects will follow fairly logically from there.