Three years ago we shipped our daughter's car from N CA to NC & we used TNT Auto Transport. We'd use them again.
The uniform key we found for all these places:
1. give them LOTS of time - our daughter's car was picked up from a locked lot - we left it at in Santa Clara, then the truck went to WA, NV, WI, IL, NY, NC, VA, FL. They go all over the US to pick up & drop off these cars. We had no time issues, so they gave us a 5 day window & we kept checking. They picked it up on day 4. They gave us a window on the other end - it got there before the expected date. If you don't pick it up after the window ends, you pay storage fees. If they're late, they pay for a rental car.
2. its cheaper if you don't have door-to-door service. We dropped the car off in a lot, which was secured at night & it was dropped off in Raleigh-Durham at a used car dealer's lot, which was secured. It was washed for her before she picked it up.
3. realize they will drive your car "a bit" - but it should not be much...only enough to get it on & off the truck so they can pick up or take off another car. There are lots of stories about cars that are driven around, etc...Most good companies note your beginning & ending mileage.
4. make sure you have a # you can call everyday - weekends included - & try it FIRST, before you commit. Give the company a call, you'll get a recording, but if it asks if you want to be connected to a "locator" - try it. Some companies don't have someone who is available to "locate" where your car is. Thats how we knew where her car was...she called just to check - they didn't mind & they understood....and, she got to know the dispatcher (which might have facilitated the car wash at the end - who knows).
5. don't ship stuff in your car, unless you've paid a premium for that service. These are auto shippers - not moving companies & the good ones will tell you up front they have no liability insurance for anything which is taken out of your car. So, if you're planning to move your HDTV & stereo equipment - you'll take the risk. We also had a weight limit, so if you have an SUV, you'll pay more. There is only so much weight these trucks can carry.
6. there are open & closed carriers. Unless you have a vintage or really expensive car, the risks of damage using an open carrier is no more than driving.
Now - the bad part. Three years ago, it cost approx $1850 for drop off "nearby" (really local) & pick up in R-D (2 hrs from where she was going to school), which was not an issue since drsdn flew with her to help move the heavy stuff - they just drove to RD & picked up the car. It took 3 weeks - so allow plenty of time. This price & time frame was in the ballpark of all the ones with a good reputation. But, it was far, far cheaper than having me or drsdn drive across the country with her & we got to have her home for a bit more...so it was worth it.
Good luck!
