Yups,

Any car you like. As long as it's in good shape.
We used a lada break in 2007 (too long ago...).
https://www.flickr.com/photos/nadjen...57603287199966
And that was standard except from removing the rear seats.

I'd go with any lada in good shape again anytime. Most locals drive them, meaning that the roads tend to be just smooth enough to pass trough, mechanics understand them, and maintenance is cheap, and spares, if needed are readily available. Big advantage is that you don't stand out. By the time "they" realize you're a foreigner, you're past the checkpoint. Obviously, there are limitations too. Some of the out of the way places cannot be reached in a regular car (e.g. Mountain villages, or the darvaza gas crater), it will demand more driving skills and care when it gets rough, and you have less load carrying capacity (think backpacking when packing your stuff, and there will be loads of space left for comfort and treats.

If you want some more ground clearance and storage, I'd think a Honda CRV or toyota RAV4 wouldn't be bad. I've seen them around there, so I guess spares won't be to hard to find. You can't do much wrong with a toyota hi-ace either.

Land Rovers/cruisers/ nissan patrols... will carry whatever you want, as far as you want, and where you want, and they do look good on the pics (a factor I'd consider. They stay around long after your trip), but they also cost a bit (both in acquiring and maintaining). All are perfectly suited the way they come from the factory.

A lot of Vans and 4x4s have been abused. And a car that has been abused will cause much more frustration than any other car in good shape.

In the end it very much depends on where you want to spend your money on, and what makes you feel good. Most people leave very much over equipped.

Enjoy!