The Marina would be most convenient if your classes are near Fisherman’s Wharf, but I find that the atmosphere there is a lot more yuppie/preppie and the social scene is not nearly as interesting as what you’ll find in the Mission, Lower Haight, Duboce Triangle areas.
The Mission has lots of funky thrift shops and restaurants and art studios and cheap taquerias and bars, and you’re likely to find something relatively affordable (i.e. $800 per person) in that area sharing an apartment with a bunch of other roommates. The Sunset has good deals but it can be much more foggy there and it’s also pretty inconvenient for getting to the Fisherman’s Wharf area.
If you live near Fillmore Street (in the Lower Haight or Duboce Triangle) or in the Mission area near 16th street, you will be near the 22 bus line, which runs all the way to the Marina (about 30 min on the bus). So you might want to look for something near the 22 bus line and then it’s just one bus down to that area.
Public transit is relatively good here, but if you’re used to NYC you might be disappointed. If you think you are going to be spending late nights in your art studio in Fisherman’s Wharf, you might actually want to bring your car. The buses run very infrequently late at night (sometimes after 10pm the 22 comes only every 40 minutes). I have lived in SF for 6 years without a car, but I think if I were going to be going back and forth frequently from the Fisherman’s Wharf area to the Mission, a car would be useful. However, renting a parking spot in SF will usually cost you an extra $200 per month.
Another idea would be to find a month-to-month sublet for a few months while you get to know the city, and then after you’ve been here for a few months you can find a place in a neighborhood that you like.