Hi JordanSker--
I agree totally with the advice given by Non-non rev.
One caveat: Allow plenty of time for taking the C shuttle between the airport and the LAX transit center. Although the shuttle is supposed to run on a schedule, it can get really whacked out by congestion at the airport. I have had a few REALLY close calls using the shuttle for flights (at least the Coliseum won't take off without you!). On your way to the Coliseum, I would allow a whole hour to get from the airport to the 42 bus using the shuttle--this may be WAY overdoing it, but it could take that long.
There is no charge for the shuttle itself. You need exact fare for the bus.