A big thanks to all of you for all of this helpful information and advice! A few responses:

My first inclination was to just get on my bike and go. The Natchez Trace Parkway is my goal for when I'm ready to tour alone. I've been reading up on bicycle touring, and the amount of information - sometimes conflicting information - is a little overwhleming. I was looking at an organized tour as a way to get a crash course from experienced people - an easier, hands-on way to figure out best practices, what mistakes to avoid, etc. Also, although I am darned near fearless in most other aspects of my life, I am a bit apprehensive about traveling through small towns and out-of-the way places alone on a bike. Even when I take road trips, there are still certain sections of the state/regional where I wouldn't really feel comfortable stopping. So, I thought that being with a group might help allay those fears. I am more interested in self-supported group tours than van-supported, since I would be by myself on any future tours.

As far as tour length, anything from a few days to up to two weeks would be fine for now. I don't really have any budget constraints. I like the idea of looking for a multi-day event and booking motels instead of camping. I hadn't even thought of that as an option, which is why I started this thread. I needed a little help coming up with solutions that weren't readily apparent to me.