I have used Reliable twice, excellent communications and results......on the costly side but it depends what kind of car you are shipping of course. Also, they do not particularly want to deal with single car orders as they prefer multiple car shipments, however, when things are slow they are very happy to take your load.
Another I have used is Tropical Auto Transport out of Orlando, also excellent results.
Problem is most of the "auto transport co's" you see advertised are brokers, not trucking co's, but hey are not all bad. There is a "load board" onto which they all post their loads and a price offer, truckers/ co's pic the best paying ones out of what's posted.
You can post on U-ship, Montway is the one that is always responding, they have their own trucks and fair pricing, I have not used them but have not heard anything bad of them.
I have used a guy out of Miami several times, he is a very good broker (also happens to be my friend's uncle) so he is straight up dude. Has never let me down out of 3 cars I' ve shipped through him let me know if you want his number.