If you go to Cheyenne and turn west (#1), it's flat, ugly, and VERY windy - not great in a truck. The portion of #1 in southern Idaho along the Snake River is also flat and featureless. The least scenic of the lot, but perhaps the one with the least steep grade.
As for #2, you'll encounter some mountainous terrain in the Missoula-Kellog-Coeur d'Alene portion, but not as steep or as spread out as portions west of Denver. Pretty country, most of it.
About #3 - you'll start out going up for a long way, then down into a mountain basin, then up, up, up again, then you stay up for a long while, gently descending. This takes you close to Breckenridge ski resort.
Heading SW from CSprings to Canon City (#4) is mostly 2-lane. Not much steep grade (a very relative term, but you have no high passes like Wolf Creek Pass) except between Salida and Gunnison, near Monarch Mtn. ski resort. A scenic drive.
I went to HS in CSprings many years ago, used to ski in either Monarch or Breckenridge (these were the cheapest decent slopes for a day trip). I've also lived in SLC and Boise, and have driven all these routes at least once (many times on some), at least as far as eastern WA.
Based on your criteria, I'd opt for #2. #1 has the least steep grade, but you'll be worn out fighting to keep a big box on the road in high winds. It's also least scenic.
As for lodging, it's abundant but pricey along route #3. You'll find less options, but at lower price along #1, #2, and #4. #2 may be cheapest, as it isn't in resort areas in CO or UT (though Kellog and Coeur d'Alene can get full of visitors in summer).
Good luck. You'll see some wonderful scenery, no matter which you pick.