I am not familiar with much of your US-35 route through Ohio, but once you are on I-77 south, you may experience slow or stopped traffic at the three toll booths in West Virginia. If you have an easy pass, make sure you have money on it and have your car registered for a possibly quicker time.
I have read about lane closures on I-77 north in WV, but I think southbound is ok.
The I-81 interchange in Wytheville, VA can be backed-up with heavy traffic at times.
Other than accidents or construction, the rest of your trip in I-77 should be simple.
If you are a noob to mountains, you may consider I-77 in West Virginia a bit curvy, but it is not bad and most cars have no issue maintaining the speed limit.
I have not driven I-40 between I-77 and Asheville, so don't have any advice for that area.
The shot on 35 in Ohio will be fine. You'll go through Chillicothe (wave at me when you pass!), then Jackson and Rio Grande (pronounced RYE-Oh Grand, not the appropriate REE-o GRAN-de). You'll cross the Ohio right at Point Pleasant WV, which is a cute little town made famous by the ohio river bridge collapse and the whole mothman thing. They have a Mothman museum there. Kitschy, but kinda interesting. A part of 35 in WV is only 2 lane, so expect to slow down for that stretch before you hit I-64. You won't be on 64 for long, maybe 15-20 minutes, before getting to I-77.