You would not be able to use a rear engine model of any kind--the engine would get in the way of loading your car.
There have been several tow companies that have repurposed school buses and chopped off a lot of the body and then installed a rollback to tow cars and have room for all of the passengers that were in the car.
I have seen both Type 'C' (conventional with the engine out front under a hood with the service door behind the front axle) and Type 'D' FE (flat front with the engine in front and the service door in front of the front axle).
Both types would lend themselves well to your purpose.
As to whether to put the car inside or chop the body, that is sort of up to you and the size of your car. Most school buses have a maximum head room in the center of 78" with it rounding off at the edges and a maximum width on the outside of 96". With those constraints it might be hard to get the car up into the bus and then to get out of the car once the car is inside the bus.
Hi BigPaul. Welcome aboard. If you do a search for Elliot Naess, the first thread is titled The Millicent Chronicles. If you read that thread it is exactly what you want and how he did it. Good luck and it is nice having you here.
I agree with Cowlitzcoach. Another issue is weight distribution. Storing the car behind the rear wheelwell could be problematic.
I might have some idea of what you seek.
Mine is an '87 Wayne Lifeguard 67 passenger bus. My car is 15 1/4' which leaves me 5 windows or 14' for the house section. Unfortunately, the car weighs almost 2 tons. That's why I have the extended front bumper loaded with the heaviest tools and accessories to offset the heavy rear end.
Also, I am barely able to climb out the window when the car is in the bus. Peasant Racing has a side door on his bus that I wish I had.
Thanks for all the responses, I'll add some information that may help with the answers. The vehicle I want to haul is a Geo Metro, I am going to build one for the 24 Hours of Lemons Southern Circuit and double use it as a ATV Toy Hauler.
Good point about the weight distribution but the Geo Metro weighs 1855 pounds. I realize that's 145 short of a ton but much lighter than most.
After looking at the pictures here and suggestion by a member of the Geo forums it never dawned on me that I could have basically portable or movable furniture to place where the car is stored. So while in travel the furniture gets stored and while at the track, that would be the "living room".