Also, would this be a one way trip or a round trip, and when would it take place?

Since you've posted this in the Fall/Winter section, you should be warned that it will likely be very cold overnight and you'd need some serious 4 season camping gear if you're planning to sleep in your car, or in a tent.

Idaho has several national parks, with Craters of the Moon probably being the most famous one near your route.

The logical order to visit would be Capitol Reef, Bryce, Zion, Grand Canyon, Painted Desert (which will require some backtracking), and Death Valley. Grand Staircase could be before Bryce or after Zion, depending upon which parts of the huge park you want to focus on.