Obviously, the buggy is a modified volkswagen beetle. And the rat-rod buggy is, well, an off-road rat-rod.

But what car (chassis) is the cuprino (and monarch) supposed to resemble?

The cuprino and monarch were muscle cars, In the world of Rage cars are recycled and made from whatever parts people could salvage, the buggy, according to the book has a hummer engine in it.

it almost looks like a roo, or el camino, or ranchero, doesnt it?
Beefed up, but a truck-car, none the less