My Mom has a 3-wheel
scooter at home that I'm comfortable disassembling and reassembling, so when we went to WDW in August and rented from Apple Scooter, I assumed that disassembling theirs for the car would be a piece of cake...
Granted I didn't invest a lot of time trying to figure it out, but the rental scooter didn't seem to be like the one I was used to. I rented a Pride Victory 10 3-wheel.
I think if you went with either the 3- or 4-wheel Go-Go Elite Traveller it would be easier.
This video shows a scooter that's similar to the one we rented.
http://www.youtube.com/watch?v=6-uaM6g_GsM
I think that if you're already accustomed to disassembling/reassembling you should be fine. It's also entirely possible that the scooter rental company could give you instruction on how to do it.
Will you have passengers in the back seat, or would you be able to use that for storage of some of the scooter parts? Keep in mind that not only are some of the pieces heavy, but they're also just big and awkward. Will you be doing this yourself, or will you have someone to help you lift?
I think you could squeak by with an economy/compact as long as you won't need the trunk space for much more, or if you also have the back seat available for cargo and not passengers.