Ok I ship cars quite often, maybe 4-5 per quarter so here's my tips and insight into this "industry:
a) For cross-country shipping there are really only the big 3 names, almost everyone else uses brokers in some shape or form. Big 3 I'm referring to are Passport, Autobahn, and Horseless Carriage. Average price to ship a car from coast to coast is $2500-2800 depending on the route you are needing.
b) DAS is a wonderful company with "ports" in almost every big city and work great for shipping normal cars (s2000, BMW, Mercedes, etc) and they contract out for door to door on high end cars like my last R8.
c) For regional shipping, there are many smaller mom/pop places like my contact who is based out of Monterey. He ships mostly up and down the west coast and is very personal meaning he is in direct contact with you from point A-B. He shipped my GT3 picked up at a dealership and met me at my final destination outside my residence.
P.S. Autobahn ship for Audi NA and many big name car companies so they are very professional and own all their own trucks. Horseless Carriage shipped my first car many years ago when I relocated and they are also great but sometimes their shipping pickup times can be like 3-weeks out so may not be good if you are in a rush. Any questions let me know, I have been doing this a long time
- - - Updated - - -
P.S. To the OP, in case you are wondering in Norcal, DAS's port is located in Livermore off the 580/Vasco road exit so it's cheaper to have the car shipped to the port there and you go pick it up vs. having it shipped to your doorstep for obvious reasons.