Figs and blueberries can be grown by home gardeners in the Chattanooga area successfully. These fruits are seldom bothered by disease or fruit worms. Birds love them both, but netting can protect the fruits. If you want quality fruit that can be picked and eaten straight from the bush, figs and blueberries will likely provide the opportunity.
Rabbiteye blueberries are ideal in this climate. Two varieties which allows cross pollination will increase yield. Selecting an earlier and later ripening variety can provide about six weeks of summer berry harvest. Blueberries require acidic soil which is what most area soils are. However a few limestone veins exist in the area and blueberries would not do well in one of those. Holcomb Garden stores will test ph of your soil free.
Mulching with pine straw or oak leaves which are acidic is good for blueberries. In most summers blueberries need supplemental watering. A drip line or soaker hose works well. After five years one or two of the oldest canes should be pruned out to stimulate new growth. Providing mulch, water, netting, and occasional pruning will likely result in fruit for years.
Figs are another fruit likely to succeed here. They tolerate acidic soil but benefit from lime or wood ash which will raise the soil ph a bit. Figs do best on more fertile soils and produce more when compost or other soil supplements are provided. Figs love heat. Growing them next to a south facing brick wall is an ideal setting. One issue with figs is cold tolerance. Colder than normal winters kill above ground growth of figs. They grow back from roots, but produce little the first year after a hard winter. We have now had two successive winters in which many figs died back to the roots. In my previous 10 years here it happened just once.
Brown Turkey is usually the most productive variety here. Celeste has smaller fruit but is slightly more cold tolerant than Brown Turkey. Celeste fruit have a pink center and will make a reddish preserve. Mission is a favorite variety for flavor, but is not as cold tolerant as others.