Last September I joined a friend in riding the Trace. He started at the beginning and I joined him in Lawrenceburg, TN. It's a great, relaxing ride. Miles of unobstructed road.
My suggestion would be to get a map and read up on the history along the trace. We missed a few stops early on when we didn't check out the sights. We found a great little museum just before crossing into Mississippi. Read up on what we'd be seeing and slowed our pace. Took us two days to get to Natchez, then a day visiting Vicksburg's battlefields, Windsor Ruins (an off the path site, but worth the stop), and Port Gibson. Wished we could have spent more time around the Jackson area.
Cypress Swamp is very cool (just north of Jackson) and worth time spent walking the paths). Watch for the signs for some of the original Trace. Puts it into perspective how basic it was as a transportation route.
Enjoy. I'd love to do it again someday if I ever get back down that way.