The closest BART station will probably be the Embarcadero station and if I remember correctly there is no praking station there. Your best bet would be to park at a garage and to be honest if you don't need a car to get out of the city for anything it would be ideal not to have a car. The city mass transist cababilities are quite adequate to get around in San Francisco and the city is small enough, land wise, to get around on foot if need be.
I will be at the game on Sunday, taking the wife to her first game ATT park. We plan to make a whole day of it, get to the city early eat some dim sum for breakfast then poke around the city for a while. Just before the game starts we will probably stop at Gordon Biersch,http://sanfrancisco.citysearch.com/profile/876108
, for a beer and snack.
Have a good time.