Living on the Peninsula halfway between SFO and SJC I've flown in and out of both airporst. I've also sailed out of San Francisco, but we left our car at a relatives house in San Francisco and they took us to the pier.
I'm not sure that Amtrack is a good choice becasue it doesn't go into San Francisco. You'd have to take get off in Oakland or Emeryville, get on an Amtrack Bus to the transbay Terminal and then have to get a bus, trolly or cab to the pier. If you want to take a train you should take the lightrail from the San Jose airport to the Caltrain station in Mountain View then transfer to the Caltrain to San Francisco where you'd need a taxi to the pier.
My advise is to check online for airport shuttle services that go from San Jose to any address in San Francico. Check with Supper Shuttle. You can also save some money if you book round trip.