If I only had a carry on bag, I'd take Uber Pool or Lyft Line. The chances are very good that you wouldn't have any stops, or perhaps one stop on the way to your hotel. Pick up spots are easily located at OAK.
Re: BART, from Coliseum Station (where the airport line drops you off), at least there are two trains that operate at all hours going to SF, so you shouldn't have to wait too long.