I agree with PTravel. Southwest Airlines and Oakland are not worth it.

You can check the various airlines "web special" sections on their websites. Otherwise most other rates are published on all the usual sites.

All of these fly between LAX/BUR and SFO:

Delta
Alaska (use your BA miles here)
American (OneWorld, miles again)
United
Virgin America

Check the aircraft type of you don't like small planes as some of the Delta, United and American flights may be on smaller aircraft.

Alaska and Virgin America are the best IMHO. Virgin America is all new, and Alaska is a well thought of "regional" airline though they do fly across the US a little too.

Do not fly into Oakland, the shuttle then waiting for BART is a nightmare, that BART station is particularly awful. Not a good introduction to the city at all. Take your chances with any delays and fly in and out of SFO. Beautiful airport. You'll walk or take the monorail from the domestic terminal to the International terminal (stop and see it) then BART into the city.

Book a hotel that is 1-2 blocks from any of these BART stations:

--Embarcadero
--Montgomery
--Powell

and you'll be located centrally and not have to walk far with luggage and have an easy route back to the airport too.

Some notes:

The blocks on the south side of Market are twice as long as the blocks on the north side.

There is also a San Francisco city-only metro called MUNI that shares the same tunnel under Market Street with BART, but does NOT have airport service. Don't mix them up! The stations are underneath each other, but with some shared entrances.

Don't miss the Ferry Building on the Embarcadero (the name of the waterfront). Great restaurants, artisinal foods, and a farmers market.