I paid $600 to ship a car from Orlando to SW Michigan. The easiest way to find a good company is to ask around at your nearest auto auction. Cars are regularly shipped all over the country and a majority of the shipments of used cars originate at the auto auctions.
It might cost more to ship just a shell as the trucking companies intend to drive it onto the car carrier. Shipping a shell might require a flatbed truck. If it has wheels and can be easily pushed, you might be okay. Be sure to specify the condition of the car when looking for a carrier.