Really, there's no reason not to use the Ferry Building (SFC) stop. It's the only place with checked luggage, and it's also really well-positioned in terms of transit. You're right at the end of Market Street, near the end of several useful Muni bus lines and the F streetcar and just a block from the Embarcadero Muni/BART station.
This is all if you're staying in The City, however. If you're staying in the East Bay, I recommend detraining at Richmond (no checked luggage) and grabbing BART there. (The Amtrak and BART station are one and the same.) If you're staying on the Peninsula, detrain at San Jose and take Caltrain up. (Once again, Amtrak and Caltrain stop at the same station.)
As far as your options from LAX-SFC, you basically have two choices- the
Coast Starlight or the
San Joaquins service. The
Starlight is a beautiful trip, and is all one long-distance, comfy Superliner train, but it's almost precisely 12 hours- getting you in to the Bay Area around 10pm. The
San Joaquins are much quicker, with #715 getting you in to town just past 7pm, but the scenery is somewhat less than ideal. (Endless farms and mostly small towns.) There is also a 3-ish hour bus ride between LA and Bakersfield- the buses are clean and comfy, and the connection is guaranteed- eg, the train will wait for the bus if it is late- but some people really dislike riding buses. I also believe there is a slight price difference between the two options.
Aloha
Another Option is get off the train in Oakland and take the ferry across the bay to SF. At the time I was there the ferry fare included a transfer to the SF Transit. The ferry docked in Oakland about 3 blocks from the train station.
The
Alameda-Oakland Ferry runs on a relatively limited schedule. You can't catch it off the
Starlight, but you could catch it off the
San Joaquins on
weekdays only. Also, transfers to Muni (SF's transit system) are only included for holders of weekly or monthly passes, though all tickets include a transfer to AC Transit (the East Bay bus operator).