Barring road construction (don't know) 287 and 220 should be fine. The only problems I've ever had on that stretch was during the winter. The others you mention should be okay, but it's been a long time since I've driven any them any distance. That's the route I'd probably take if I were you.
Hwy. 16 between Newcastle and Custer is a mess right now from extensive road construction. I'd avoid it if possible, especially with a motorhome/camper.
From Casper you *could* take I-25 north to Buffalo where you'd take I-90 east. Or to save quite a bit of time, you could take I-25 from Casper to Hwy 387, then take it to Hwy 50 or 59 to Gillette and pick up I-90 there. 387 has some dips and bumps in some sections, but it's not bad. Hwy. 59 is a better road than 50 but is also busy, so I normally prefer Hwy 50 going that direction.
Most of Wyoming's state and U.S. highways have plenty of room for any camper. They get lots of truck traffic!