I think I would be afraid to drive on roads like the Trail Ridge Road and the Road to Mt. Evans. What is normal driving like? Say I wanted to go from Denver to Breckenridge or Crested Butte.

These are really destination roads, not routes from one place to another, except Trail Ridge Road, which links the eastern and western slopes in the summer months. Basically, both roads are closed as soon as snow falls (Trail Ridge opens earlier and closes later than Mt. Evans).
Trail Ridge is easy to drive, Mt. Evans is a nail-biter.

BTW, you would take I70 to Breckenridge or Crested Butte (to start).

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I-70 goes most of the way to Breckenridge. It'll only cover a small portion of a ride to CB.

"Normal" driving is weather dependent. WHEN ARE YOU GOING?

October 14-22

No one can answer that question without knowing when you want to do this drive. Driving to Breckenridge from Denver is not difficult in the summer, for example. I drove that same route last March (with someone who was driving, anyway, I wasn't), and it wasn't difficult but we got lucky, as there was a big snowstorm one night that shut I70 down for a bit (more towards Vail, I think), but luckily it was over on the day we needed to leave so no problems. So it's not difficult except when there are weather problems. It's a major interstate to about Frisco, but then the road coming down to Breckenridge isn't difficult in good weather, either. It's a regular paved road (Rt 9).

They are paved roads that are at high altitude. You want to watch the road and let your passenger do the "seeing"--at least that was my feeling. They aren't 4WD roads!!
I've been on I70 when I needed chains and when I needed to get to DIA in a blizzard!!. Colorado does a good job of road clearing or advising you to stay OFF of the roads, IMO.

I personally find driving I-70 more stressful than most Colorado mountain roads - all that thundering heavy truck traffic zipping along at high speed. Gives me the heebie-jeebies.