Sorry- I got so into describibg the Aquarium, I forgot to answer your questions!
The closest Marta station is a couple of blocks away from the entrance. We decided to drive instead. The parking deck is right next to the aquarium, but it costs about $8, I think. The new World of Coca Cola is being built right next to the Aquarium, but it is still under construction. The older World of Coke is a ways away, near the CNN center and Underground Atlanta. The Five Points Marta station is the closest to World of Coke.
Other things to do along the Marta line would be Underground Atlanta, the High Museum in Midtown, Centennial Park, and if you want to transfer to a bus, the Atlanta Zoo.