We are driving the the port (only about an hour away), but most people, including ourselves, use Super Shuttle here in town. Prime Time Shuttle is the other big shuttle service in town. I would contact them regarding their rates to the peir. Where ever you are staying (I assume somewhere between LAX and the port) will be around 30-45 mins. Taxi would be way to expensive. Limo service would be the best if it is economical for your group, but one of the two shuttle services would be a better bet.
Roger