Dallas side or Fort Worth side
Dallas side, Love Field: about six miles from downtown, with Southwest nonstops to Atlanta, Milwaukee and Phoenix.
Fort Worth side, or anywhere in between, DFW Airport: it sits between the two cities and is American's largest hub, with nonstops to all three.
Direct rail runs to DFW: DART's Orange Line from downtown Dallas to Terminal A, the Silver Line from Plano to Terminal B, and TEXRail from downtown Fort Worth to Terminal B.
One catch: the TRE train between Dallas and Fort Worth does not run on Sundays (State Fair weekends excepted), so plan the ride home from the airport before you fly.
March at both ends
Atlanta in March: highs in the mid 60s, nights in the mid 40s, and one of the city's wetter months, so pack a rain layer. The Atlanta page has the pollen details if spring allergies hit you.
Atlanta runs about four degrees cooler than DFW in March, so keep the layer. North Texas storm season usually starts in late March too, so give the flight some slack.