The easiest and quickest route would be I-75 to I-40 but taking hwy 64 thru the Ocoee gorge and 74 from Murphy thru the Nantahala river gorge (both areas haave a lot of rafters & kayakers)and past Cherokee will make for a very scenic drive. I wouldn't pull a large RV along that route, although some folks do. You will be fine in your Class C. As stated, it will take a bit longer to drive 64 and 74. If time is of no concern, I highly recommend the scenic route. You could stop in Wesser,NC along the Nantahala river and grab a bite to eat while watching the kayakers and rafters go by. Have a nice trip.
Forgot to mention that the "newer" hwy 74 by-passes Cherokee and becomes a 4-lane. It is curvy thru the Ocoee river gorge; but your Class C will be no problem. Truckers use that route also. After you get past where the 1996 Olympic course was built on the Ocoee, it becomes 4-lane thereafter till you get past Andrews,NC., then 2-lane thru the Nantahala gorge and 4-lane again before Cherokee.
I can't see how it would be shorter by going I40. 64 74 is a straight shot. wants you get past the Ocoee area it is four lane all of the way. Until you get to the Nantahalla then when you get past there it is back to four lane. Just don't hit those areas on Sat or Sunday.
Even with traffic you will have no problem with your C.