Welcome to cruise-chat! Barring any problems with the disembarkation of the previous cruise, you should be able to board around noon. One of the nice things about the San Francisco Port, is that if you are unable to board when you arrive, you can always check your luggage with a porter and spend time along the wharf. There is plenty to see and do.
As for luggage, it is always wise to bring a carry-on with you. I always pack whatever I would need to get me through the first day of a cruise (casual day wear, bathing suit, something to wear to dinner, toiletries and meds). Then I can enjoy the day, without worrying about when my luggage will arrive. You would not be able to bring all of your luggage onboard with you as they must be able to pass through security screening (same size as the scanners used at airports).
Ooops -sorry Tom for duplicating the information, we must be posting at the same time. But, I guess it is better to have the information corraborated.