I'm considering a new AWD explorer with tow package. It's rated at around 7200 lbs.
I don't know why Ford would rate a midsize SUV with a soft suspension and relatively short WB with such a high rating. Common sense dictates that doesn't make sense. For example, my F-150 SuperCrew with a significantly higher GCVWR, significantly longer WB, significantly wider track, and lower CG is rated at 5200 # MTW, and I believe it.
Should I be looking at some other vehicles? My price cap is 35K.
Like others have said, you've got 2 basic choices for hauling your 3500# car.
1. Open trailer w/ V8 full-size, I would opt for any 3/4 ton or a 1/2 ton with the biggest engine, tow package, etc.
2. Enclosed (how big is that enclosed?) with a diesel 1 ton. Maybe you could get by with a V10 if the enclosed is relatively small (i.e., 8.5x20).
Someone mentioned it's nice to separate the greasy, nasty-smelling cargo from the passenger compartment, and I whole-heartedly agree with that one. Add in that finding a heavy duty SUV (i.e., a lightly used 2500 Suburban or a 7.3 ('01-03) PSD Excursion) is not exactly easy or cheap, consider a crew cab full size truck and/or store as much as you can in/on your trailer.
For trucks, I don't like caps, it's annoying to crawl around in those, and cuts your visibility out the back window. I've got a hard cover for the bed, with a bunch of bed dividers made out of 2x4's and most of my wrenches and sockets in roll-up pouches attached to the tailgate. As such, I've got plenty of dry, organized, and locked storage for gear, tools, tires, etc. before even thinking of storing anything on the race car, or trailer, or passenger compartment (which seats 5 comfortably).
If you get a truck that does NOT have an unusual bed like mine, hard locking lids for your truck bed are not too expensive. My only option was a $1100 fiberglass ARE lid; most truck with standard boxes can get something akin to the Roll-Bak aluminum spool for under $800. Or, depending on how much storage your trailer has or can have, stow everything on there.