If your builder only put one layer of drywall, I would suggest adding a second layer of drywall to help limit low frequency transmission through the wall. Is this garage bay next to your house or an outside wall. In either case you probably want to minize sound leaking through the wall.
The usual suggestion for home theater walls is to use two layers, the outer layer is 5/8" and the inner layer is 1/2". Then you could add at least 1" of Insulshield below ear level on the sides and back and one the screen/TV wall.
You also need to think about the floor. While you could put carpet and padding directly on the concrete, carpet installers don't like installing on concrete because it is a pain to attach the carpet tack strips to concrete. If you live in a cold climate you may want to build up a subfloor so you can put insulation beneath the floor. To build a subfloor you probably want a few layers to add weight and limit low frequency sound getting through the floor and reverberating in the hollow spaces between joists.
You definitely want thick padding for carpeting, or perhaps a double layer of padding.
For the floor you could sandwich sheetrock between ¾ “ plywood tongue and groove, or 5/8†particle board or MDF. MDF or particle board are preferred because they are cheaper and heavier. You could add layers of roofing felt to the sandwich, but in your case that may be overkill.
For better sound isolation, you could float the floor. That means it is not attached to the structure below, but instead the floor joists rest inside U shaped holders. The U shaped holders could be made of MDF, particle board, or rubber. Auralex sells rubber ones. Again, floating the floor may be overkill for you case.
Look for carpeting prices in Georgia. Some people use commerical carpet which wears well. I don’t think the type of carpet affects the acoustics much.