There are very few companies who actually ship. There are tons who broker the shipping. The cheapest is by using trains and going terminal to terminal, which entails a towing cost on both ends. Ask the company if they use trains or trucks. San Diego has the terminal near downtown. They will gather cars over several days or weeks then load them all up and take them at once. It's the same for trucks. They don't want to go across country unless they have a full load. The trucking companies will offer door to door service at added cost. Everybody will try to stick you with a fuel surcharge. Get insurance. Ask if the car will be changing trucks. Just like flying, a non-stop is best. Everytime the car is moved from this truck to that, there's the chance of damage, especially a low race car.
MAKE SURE YOU READ THE FEEDBACK ABOUT THE COMPANIES ON THE WEB. That will also help you to ask the right questions. When I researched this last year, the cost was between $800-$1200.
Good luck.