Welcome aboard the RoadTrip America Forums!
The main thing to keep in mind on your first major RoadTrip is that there will be many, many more IF you enjoy this one enough to repeat it. So don't try to jam too much into this initial effort or you will simply turn yourself off to future endeavors. A simple, basic plan would be to use the old US highways that have been superceded by Interstates which often run parallel to the old roads just a few miles away. In your case, the 'direct' route would involve US-24. US-25, US-42, and US-31 down to Nashville. Because of the pace set by these roads, which is what you say you want, you'll need t budget at least two full days for the drive plus stops which might includeGreenfield Village, Wright Brothers locations and the Air Force Museum in Dayton, and Mammoth Cave National Park.
You could easily head east after your time in Nashville and take similar roads on the way home while following the Appalachian Mountains northeast through Great Smoky Mountains National Park, Mount Rogers National Recreation Area, New River Gorge in West Virginia, and maybe even the first producing oil well in the world in Titus City, PA.
In the same vein, trying too hard to save money on overnight stays by sleeping in the car in truck center parking lots is not going to add to the pleasure of this trip. Decent motels can be had for $50 a night or less. Do a rough itinerary for your trip and figure out approximately where you'll end up in the evening and then do some on-line shopping to find a good rate. Often your best bets are out in the countryside near major highways rather than in cities or towns.
AZBuck