I moved two cars by carrier when I moved from Los Angeles to Atlanta. From the research I did at the time, the most important thing is to work directly with the transport company, not a reseller. I used a different company for each car and had a vastly different experience between the two; however, one cost over twice as much as the other (guess which one the Mustang went in) 

For the wife's minivan, I used Dependable Auto Shippers. It was about $600-something for an outside transport. I had to drop the vehicle off at the nearest DAS location, where it proceeded to sit for over three weeks before ever hitting the road. I guess they waited until the right number of cars fit in with the route. The actual travel time was less than a week; however, I was without the van for almost a month. This meant that I had to rent a minivan in the mean time. This put the true cost to me at a bit over a grand.

The Mustang was shipped via FedEx (no joke). The whole experience was an absolute dream. They came to my house and loaded the car on the elevator and into the top of the enclosed trailer. The driver gave me his cell phone and told me his planned route. I could track it online along the way. He showed up at my house on the day that he said he would, 4 days later. That said, it cost about $2,000