Auto transport companies vary widely in their service. Those with low rates either sub-contract their work to other carriers who then put you on stand-by, that is, you wait for a truck with open space that's headed your direction, or they're a mom and pop operation with smaller units and you again wait for a slot. If you're in no hurry it's no big deal but it can be frustrating. I contacted to have a BMW sports car brought to Ohio from Palm Desert CA and it took them almost 3 months to get the car to me. It didn't matter as it was winter when I contracted with them so by the time the car got here, the snow was gone and I was able to enjoy the car. My advice, get it in writing...ask the company to give you window of pickup and delivery in writing so you know when your car is on it's way.
As for who to use, there are many to choose from on the internet. Companies like Intercity Lines are top notch but you will pay for that service. I used DAS Auto Shippers for another car haul but it was only 300 miles...and service was prompt and reasonable.