When to go to the South
Any time in between April and November would be a good travel time. Although temperatures rarely drop below freezing in winter (except in the mountains) you won't see the rich vegetation of the south at that time. And this is really an amazing sight you shouldn't miss. I would recommend to travel either in April/May or September/October. The temperatures are not as high as in the summer and the humidity is still low which in turn results in clearer views from the lookouts in the mountains. Especially in July and August the weather is a real pain: temperatures above 30 °C, 100% humidity and usually heavy showers in the afternoon. Believe me...you don't wanna hike under such conditions.
Getting to the South
Atlanta is the ideal starting point for tours through the south. It's an amazing city, has lots of rental car companies and is the shortest flight connection from Europe. One usually has to switch planes in Washington, D.C. Flight time is about 9-10 hours from Germany.
Getting around in the South
Atlanta has a public bus system but I wouldn't even think about using it permanently. I had to use it a couple of times though (before I bought myself a car) and my impression was that the bus schedule is rather a suggestion then a reliable time table. Besides, it takes you hours to get from one point to the other, since Atlanta is simply too large.
As far as I know, there is no bus connection outside the city, except for companies like Greyhound. But I highly doubt that you can get to the places I describe on my website by bus.
There is the usual US air traffic, which allows you to go to almost any location by plane. Airfares can get as low as 50$ (one way) to destinations like Charleston, Savannah or even Miami. Always check on specials, it might be worthwhile.
A car is a definite MUST in the south! Especially in Atlanta you're lost as a pedestrian! Outside the city center boardwalks simply end and you have to continue on the highway. No way to get to interesting points outside Atlanta without a car!
Rates for rental cars start as low as 15$ a day (plus insurance). They usually also have specials where you can get rental cars for 200-300$ a week.
Camping in the South
There are lots of State Parks all over the south. Almost everyone has a campground and if not they can tell you where to go. Prices range from 10 to 15$ a night (one tent + person + car). They are usually well maintained, provide all the necessary facilities and have firepits where you can also grill your steaks.
If you're not able to find a campsite or if it rains too heavy, there are also reasonably priced motels along the highways. Prices between $30-50 a night for a double room.
Groceries and prices
Every town has at least one supermarket with the usual US selections and pricings (a bit more expensive than in Germany though). Even in the mountains there are always bigger towns with more than one supermarket where you can get anything you like.
I hope, that helped a little bit for those of you who are planning on going to southeast of the States. If you have questions, email me.