We have done similar trips several times, both in our van and the last 3 times in our Class C. Much of the recommendations I have will depend on your time available to travel.
Across the Top: Stop at the Visitors' Center on I90 in South Dakota that sits just above the Missouri River for some info on Lewis & Clark's journey, and a nice view. Drive thru and marvel at the Badlands NP, and upon exiting visit Wall Drug for a bit. Drive on to Rapid City, see Rushmore and also the Crazy Horse sculpture under construction. Drive on to the Sundance WY area and take a side trip to see Devil's Tower NM (the monolith featured in "Close Encounters of the Third Kind". Drive on to Cody, WY a spend a few days here. The Buffalo Bill Museum in first rate, and it can take a couple of days to see it. Head into Yellowstone via the East Entrance. (The drive from Cody to the East Ent. YNP is spectacular on it's own). Spend time in YNP, then head south to Grand Teton NP and spend some time here and in Jackson WY. From there take a route you wish to Idaho Falls, Idaho that sits on I15. You can then go to any number of ways to Oregon, California, Las Vegas, and other points west.
The Middle: Use I40 for your return and do stop at the Grand Canyon. From here, you can make several side trips depending on your time available. You could go to Zion and Bryce Canyon NPs, go to Monument Valley (highly recommended), Mesa Verde NP (recommended), 4 corners (OK), Sedona (recommended). If you keep heading East on I40, you will come to OK City. There is a very nice Western/Cowboy Museum in town that is worth the visit. As you continue East to Nashville, you will find steadily increasing truck traffic from about Little Rock, and increasing significantly as you approach Memphis. Memphis to Nashville still heavy, but not as bad as the LR to Memphis segment.
Hope this helps.