Whatever you do - get covered, single-destination transport. I made the mistake of allowing Dependable Auto Shippers transport it on a regular carrier from CA to MA. They ripped off my apron (and threw it away), in turn destroying the apron mounting points in my bumper, took the car for a joyride and left it covered with mud when they delivered it (the other two cars transported with it didn't have a spot of mud). Once the mud was cleaned off, I found that there were scratches into the paint on almost every body panel.
After getting a quote for $5800 from my body shop to repair all of the damage they did (not even a full respray!), they offered me $2100 to replace the front bumper and the apron - the only two pieces they would admit to damaging.
I'm in the process of getting the car repainted over this winter and didn't get to drive it in the summer/fall due to waiting to settle my claim with the transporters.
Long story short - Single-destination, covered transport. No loading/unloading.