Personally, I would recommend you begin your search with Inner Richmond, Laurel Heights, or even the Haight. Those will afford you the opportunity to walk to USF. I used to work there and lived near Arguello and Geary. It took me 20 minutes from there up the Parker Street hill.
If you can't find anywhere between there and the university, start looking at outer Richmond. Especially on any of the Avenues. The 38 bus will drop you off at Geary and Parker. The further out you are on the Avenues, the more options you might have. Remember though, most folks in SF consider the Avenues to essentially be on the moon.
USF has very limited parking and if you try to drive there everyday, you will more likely drive yourself mad. Wherever you choose, make sure there is a bus route nearby.
Sunset will also be an excellent choice because the park is essentially between you and the university.
Doen't even need repeating that you will need more money than you think to live in SF.