Back in 2014 I did a trip from Denver to Portland and vicinity.
I have two rules I try to follow, but sometimes have to make exceptions.
Rule #1: No interstates
Rule #2: No night driving
In your case, I might be tempted to violate Rule #1 in the flat bits of the Dakotas and Montana. I have a "Hierarchy of Lotus Roads". Worst are Interstates. Too much truck traffic, too straight and flat. US highways are better, but still may have many large trucks. Numbered state routes are best. Minimal truck traffic. Numbered county routes may require local knowledge, as they're not always paved.
But I'd recommend keeping Rule #2 violations to the minimum. First, for me, one of the main ideas of the road trip is to see the country. Can't see it very well at night. But more important, perhaps, is wildlife.
I blogged that trip and posted links to each entry here: Epic Northwest trip
My route and your proposed routes don't have a lot of overlap, but you may find some helpful info in there somewhere. I found some nice Lotus roads in Oregon, followed parts of the Oregon Trail and the Lewis & Clark Trail, and visited Grand Teton NP.
See here for how I packed the car for a couple of extended road trips:
Portland trip prep
Laguna Seca trip prep
For a long road trip like this, I'd go with a UHP summer tire rather than the stock tires. I've only been getting about 5k miles on the rear tires on the stock Yokos. For both these trips I ran on Dunlop Direzza DZ102 (actually 101 for the Portland trip, but the 102 replaced the 101). You won't need a higher performance tire for the road, and these are better in the rain than the stock rubber. I'm aware that almost nobody on this forum likes the Direzzas, but so it goes.
Most important, though: Have fun!