Car Delivery companies are either bespoke car delivery businesses or they are recovery companies making use of the equipment that they already have. Bespoke car delivery companies are usually a little cheaper as they do not have to have as much heavy equipment and overhead to cover. However, there are many more recovery companies out there so finding one will be easier.
You do not necessarily require a very large electric winch to recover cars onto your transporter. Smaller 4x4 style winches will do the job but be aware that the drum speed may be much slower than that of a larger winch.
A large 4x4 vehicle is your best bet when considering a tow vehicle for heavy towing. Smaller 4x4s and sallon cars do not have the legal Train Weight to enable you to tow a car on a trailer.