South San Francisco - BART station - was created in 2003.
San Francisco International Airport - SFO - - BART station - was created in 2003.
I would recommend BART. The South San Francisco BART station is at 1333 Mission Rd, South San Francisco, CA 94080 while BART has stations at Civic Center, Powell & Market, Montgomery & Market, and the Embarcadero.
Fremont - BART station - was created in 1972.
Lafayette - BART station - was created in 1973.
BART stops at the Embarcadero in San Francisco, which is full on hotels.
Bay Fair - BART station - was created in 1972.
North Berkeley - BART station - was created in 1973.
West Oakland - BART station - was created in 1973.
El Cerrito Plaza - BART station - was created in 1973.
El Cerrito del Norte - BART station - was created in 1973.
You can find secure lockers for storing your belongings at San Francisco Airport in the International Terminal near the BART station.
To get from Berkeley to Oracle Arena, you can take the BART (Bay Area Rapid Transit) train. Board the BART at the Downtown Berkeley station and travel southbound towards San Francisco. Get off at the Coliseum station, which is the closest station to Oracle Arena. From there, it's a short walk to the arena.