I've driven several routes including the one posted by perdidobay. After getting to Birmingham, I prefer to take I-65 south to Montgomery, then Hwy 231 through Dothan to I-10. Take I-10 East to I-75. This route is about 50 miles shorter than going through Atlanta. Most of Hwy 231 is 4-lane, 65 MPH speed limit, but there are a couple of towns and traffic lights. Takes us about 14 hours including a couple of short stops for fuel and meals.
Going through Atlanta is all interstate, but depending on when you go, Atlanta can be conjested and there may be heavy traffic on I-75 through Georgia. There's not much difference time wise between these two routes; going the Birmingham to Atlanta route took us a little longer than the Birmingham to Montgomery route.
Some people go Memphis-Nashville-Atlanta. I do not recommend that route; it is much longer than going through Birmingham.