The big 3: UA,DL,AA, all fly from SFO to HNL. They mainly use 757s, or 767s.
Aloha flies from OAK, and are probably the best value from the Bay Area. They reportedly have excellent service, and are not that highly priced. Unfortunately it would require your to do an airport to airport transfer, which isn't that easily done. BTW, they fly 73NG, and it would be possible to make the connection after arriving in SFO. The airport to airport transfer is going to be made a lot easier when BART finally goes through, but that's not going to happen in the immediate future (it looks nearly ready).
If your heart is set on going through SFO, your best bet is flying UA for your trip. It will be easier, and probably cheaper for you. Hawaiian is going to give you better service, and they fly either 767er, or DC10.
The Virgin/Continental service through LAX seems the best choice, but I won't blame you for avoiding LA if you choose. (LA should be avoided at all cost, as it is LA).