I lived in Chattanooga from late 1983 to early 1995 out in East Brainerd. Chattanooga is very hilly in many places. I was able to cycle from East Brainerd to the Missionary Ridge area by way of Shallowford Road. Traffic was tolerable, but I did it outside of the rush hour. Many streets and roads in the Chattanooga area are a bit narrow with a drop-off into a steep ditch. The speed limit on these is generally in the 35 to 45 mph range. Many drivers there are on the aggressive side. Tailgating is a sport and art form. Sometimes it is possible to work out a route that crosses the city and uses less traveled streets, but often there are only a very few arteries that cross natural boundaries insurmountable by bicycle.
In general housing is very inexpensive in Southeast Tennessee. You may be able to live in a revitalized neighborhood close to your work. Downtown streets are probably more friendly for cycling than arteries coming in from the 'burbs.'
There is no light rail system. There are busses.
As far as living in Georgia is concerned, a lot would depend on where in Georgia you wish to live and where you must cycle in Chattanooga. Take a look at a topographical map. You would not want to climb many of the ridges that populate the area. Hwy. 27 is busy but connects parts of North Georgia with greater Chattanooga while presenting a rather unhilly path.
My first-hand information is a dozen years old. I hope some of this helps.
The Tennessee Valley Authority is a major employer, but subject to the vagaries of congressional budget setting. There are also some insurance companies and other concerns there.
Southeastern BBQ is a real treat. Make sure the pork is pulled and not chopped. Pulled pork eliminates the grissle and fatty pieces.