I recently shipped a car from DC down to GA. What I learned from the experience is most of the car shippers you see online are not actually shippers. They do not own any trucks or trailers. They are brokers. There is an exchange with a bidding system. You tell the broker you need to ship a car and how much you want to pay. They tack on their fee and put you on the list. All the people who actually do the shipping look at the list to see what cars need to go where and how much the person is willing to pay.
I ended up paying about $550 to bid myself to the top of the list and pay the broker. A couple hours later, some driver picked up the job. Dude shows up, barely speaking any english. He looked fairly sketchy. He was driving a diesel van with a window AC unit mounted in it. Pretty sure he slept in his van to save on having to pay for hotels. Either way, we both took pictures before he started loading it and after he met me down in GA. No damage to my car and it made it here in a timely manner. There were automated emails fired off, so he was definitely legit and running some sort of commercial software to run his business. The emails said the business name who actually handled moving the car was TWO BROTHERS GENERAL SERVICES LLC out of FL.
Due to the nature of the bidding system, if you go that route, there are seasonal rushes. In the winter, a lot of folks from up north wanting cars hauled to the south. Then in the spring, the rush happens in the opposite direction. So it'll cost you more to move a car depending on which direction its going and what time of year.