You can take MARTA, but then you're at risk of being shot in the face.
Depending on your family type/post-game activities, you can park at the Cheetah for $3 and walk over, but it'll cost a lot more after the game.
You can also park in the Plaza Midtown retail parking, buy some candy to sneak in from the Publix. Probably your cheapest option.
There used to be a lot next to that Domino's on 14th. I've got no idea if it's still there or somebody snuck a high-rise apartment tower on there.
Despite the jovial tone of my post, believe it or not, all are legit options.
ETA: The cheapest GT option at Centergy seems reasonable at about $10/game. Midtown parking just isn't cheap anymore.