We live in the Staunton Va area, and have travelled I 64 and I 66 numerous times. On both once you get about 20 miles west of either DC or Richmond, traffic thins out quite a bit.
Your route, I 64 all the way is the easiest, and you shouldn't run into any problems at all. You'll have a 20 mile dogleg onto I 81 south to reaquire I 64, but again, no problems or road construction.
Plenty of exits for gas, food, and rest stops. Busiest area, traffic wise will be I 64 as you go thru Charlottesville between about mm 130 to mm 118. Just moderate traffic. Longest pull up you'll have is the Afton Mountain area, about mm 102 to mm 98, but there are truck lanes, and I've never had a problem with our class c towing a Subaru.