I hate U-Ship, it's mostly brokers now, you never know who you are going to get. Brokers take their $200 off the top, and put your load out for all drivers to see. Too low, and your car is going to sit for a while.
I buy, fix, and sell classic cars, usually one or two a year. I use UnitedRoad.com pretty much exclusively. You can get a quote on their website with no pressure. I have found them to be the best at actually getting the car picked up and delivered in a timely matter. They own their own trucks, do drug testing, and their trucks have always been the best I've seen. If you call them after you have your quote, they may be able to knock a little more off
I've seen a lot of trucks falling apart, leaking oil out of the hydraulics all over my street, drivers on drugs etc...