I just did that drive last month when my flight home from a cruise went haywire (long story). We did it in a rental and made it in three nights (not recommended).
I really don't like I-10, so we went up through Atlanta and caught I-40 in Memphis and took it the whole way. It was a gorgeous drive and I'd do it again. Actually, I'm doing it again for business at the end of the month (another long story) and I'll take the same route, except I'll probably come south through Alabama into the panhandle instead of going through Atlanta again.
As far as places to stay, that totally depends on the time of year you're going. I'd pick your route first, and then start calling random camps along the way to find out how full they are to determine whether you're going to need reservations along the way. You'll definitely need reservations on the weekends.
RV Trip Wizard is a great tool for plotting out your trip. You can configure this bullseye of concentric circles to whatever distances you want (200, 300, & 400) and then use that to visually see how far you think you want to go in a day, and then find camps within those ranges.
A good round number is 50 mph average. The accounts for slower speeds in an RV plus stops for gas, food, and breaks.
