I didn't pick the transport company, I don't know who it was, it was part of a relocation. We needed a tow truck (with a very good driver), a floor jack, some boards and about 2 hrs to get the car out. It turns out that the company relocation folks hired a middleman to hire the truck/driver. That really complicated things. The middleman actually told me to go pound sand when I first contacted them. I had many conversations with them and each time their attitude got worse. Apparently the relocation folks have some clout with the middleman because one phone call to the relocation folks produced AMAZING results! The middleman's attitude did a 180 and the check was in the mail pronto. Sad, they transported several cars for me and that's the only one that had issues.
I've heard stories of some transporters holding cars for ransom (twice the agreed upon price) before they are delivered. Without an iron clad contract, good legal representation, and a willingness to endure a long process (during which your car is probably stored in a battery recycling facility), they have you at a disadvantage.