Lots of pictures of huge vehicles... I think my first priority would be reliability and maintainability. If the tire can't be changed by one person using hand-operated tools easily carried in the vehicle itself, then it's not a good choice for a personal survival vehicle IMHO.
I think I'd probably start along the lines of a heavy duty chebby Tahoe, upgraded suspension, 4wd, with whatever motor runs on the largest selection of fuels. A flex fuel motor might be able to be run on a mix of gasoline and home-brewed alcohol, but post-apocalypse America might have a good supply of kerosene and diesel so it might be a good idea to have a diesel motor that could be swapped in. So your survival vehicle would need a simple enough electrical system to allow a motor swap. Better yet, gut the entire electrical system of the car and install dual hard-wired wiring harnesses to the motor so you completely eliminate all control modules and computers for the car. Basically you take your SUV and gut it no different than you would a purpose-built race car, and re-do a very simple electrical system that can be repaired with wire and tape instead of expensive computer modules.
A basic utility truck chassis might be a great place to start. Anything you can't fix yourself, and anything electrical that will disable the vehicle if it fails, needs to be removed and replaced with something simpler. And you'll need a big bin full of any spare parts you can't make yourself, like fuel/oil/water pumps, injectors, spark plugs, etc.