I had a car shipped from CA to SC in January; used a broker (Affordable Auto Transport) out of Florida, who ended up contracting with an independent carrier named Roland Hinson (hinsontransport.com).
The broker was a bit sleezy, but I had a good experience with the carrier. He gave me a well defined pick up time/location, was on time, polite, and loaded up my truck with no problems (my dad actually handled this side of things). He kept in touch with me during transport and brought my vehicle to me just as I had left it. One thing that irked me slightly was that he asked me to meet him on the interstate to save him some time from getting too far off the road. In the end, it probably worked out better that way as he would have had a hard time getting his truck around downtown Charleston. He uses an open flatbed, so if that's an issue for you, Hinson Transport may not be the best option.
Also, I guess I'll mention, the way it worked with the broker is that the guy (Tommy?) called and we talked about where the truck was located and where I wanted it shipped. We agreed on a price that was based on the mileage and posted on some truckers only board for carriers to see. According to him, we were bidding against some other jobs and needed to price competitively, but ultimately the cost was in the range I had planned for so I was satisfied with what I paid. The broker charged me a fee when they secured the carrier, and I paid the rest (majority) directly to the carrier.
Hope that helps. Good luck.