I asked this in the "where to live in LA?" thread, but can't remember what you answered.
corporate relocation?
If you do have that, look at the cost policy (talk to the agent handilng your case) They likely will be able to calculate the max they can reimburse you for driving vs flying you and shipping the car.
Advantage of driving yourself is that you have a trunk full of stuff when you arrive, instead of living out of 2 suitcases until your stuff arrives. Considerations are who are you driving with? and the time it takes to arrive, and extra miles on a nice car.
Advantage of shipping the car is speed of your time. On a corporate relocation package you get money for a rental car while you wait for your car to arrive. (the car shipment is paid for) As a guide, if you're paying out of pocket, I paid $1450+$100 broker fee for 2 cars from LA to Boston last June. Your costs will be based on what kind of deal you can work out with the guys shipping the rest of your stuff.
As for selling then buying, LA is a really big car market. With the prevelance of internet sales these days, you can pre-negotiate your car price before you arrive. As an anecdote of the advantage of the large car market, my uncle bought a Camry in LA and had it shipped to Kansas and he saved money vs buying it in Kansas. (I know MD isn't Kansas, the difference may not be as drastic) As for the dealers, there are plenty of them in the South Bay, close to the airport. There should be one or more for each manufacturer in Torrance, Redondo Beach, and Manhattan Beach. If you get a pre-negotiated price, make sure you ask for out the door cost. Don't want to be caught 11% short because you forgot TTL.