Shipping a complete car is a tricky proposition. There are transporters who will go coast to coast for around $1000, but I don't have anyone I work with on a regular basis. However, I will be happy to investigate to assist a serious buyer.
If the car you want to transport does not run, you can expect to pay extra. In that circumstance, the driver has to reconfigure his load so that he doesn't have to move your car until he gets to you, and so that nothing is behind your car when he does. Plus, he has to have help to load the car in the first place, and potentially to unload it.
You are welcome to pick up your car and transport it yourself. I do not recommend planning to fly in and drive your car home. I wouldn't do it...and I'm pretty good at roadside repairs. I've even fixed cars with chewing gum wrappers!
If you want to pick up a donor car, etc., yourself, consider renting a truck large enough to put the car inside. The rental companies don't like to do this, but I have some local guys who will work with us.