If time is of concern then do I-40. Its the most direct. The construction thru Memphis and Nashville is not terrible if you avoid going thru during rush hour times. Patience is still in order though. There are a lot of campgrounds all along I-40 so planning for reservations should not be necessary. Lots of places to stop and see too if you want to fit in some sight seeing too.
I have to agree with Tom (above post) for going thru Asheville (stop and see the Biltmore House) to US 64 in Morganton then up US 321 into Boone, its the least twisty. Just remember you are in the mountains so there is not much straight road anywhere in that area. Beautiful country there too. Enjoy.