I wouldn't build my visit solely around BART. You would be limiting yourself.
BART is a regional rail system. There are local transit systems as well, such as Muni/SFMTA in San Francisco, AC Transit in the East Bay, SamTrans on the northern Peninsula, etc.; plus CalTrain and ferries. The point being that depending on where you are going, you may end up using more than one transit system.
All the info you need is readily available on the Web. For example:
www.transit.511.org