I am contemplating using these guys to move one of my cars.
http://www.horselesscarriage.com
For normal cars I'm not picky. Classics are a different story.
You want to deal direct, no broker.
You want door to door, make sure their definition of door to door is the car goes on at the pick up and stays on till the final destination.
A lot of the brokers/cheaper outfits operate similar to FedEx. They pick up, drive to a centrally located distribution hub, unload and reload the vehicle onto another truck bound for your destination.
One problem with this approach is cars can sit in a lot until there is a load going to the destination.
I've heard of peoples cars getting stuck in distribution lots for days even weeks.