I have a very similar setup to what you're talking about.
I recently converted my garage into a recording/rehearsal room. It's a 2-car garage that measures about 19ft x 19ft.
Here's what I did:
I built a few walls that sealed off one of the doors while leaving the other one operational. This left me a little section of the garage to use as storage and work area.
For the studio room, I installed a vent in the ceiling and used a T-junction to splice into the nearest AC duct. My garage was next to the utility room, so that's where I spliced from. This required about 7 feet of AC tube to reach the vent in the studio.
I took off the weather stripping from the bottom of the door that leads into the garage (from the house). This left a 1/2" gap or so for return air circulation.
My garage had concrete floor, so I left that and treated the walls and ceiling with fiberglass panel absorbers. The room sounds great now.
Your problem will probably be with the garage door. If you want it to still be operational, that will be tough to do. I suppose you may be able to treat it acoustically with panels and secure them well enough so that they stay on when you open the door. (Obviously they would all need to be placed so that they don't interfere with the bending of each section of the door during opening.
However, if sound leakage is a problem (and you don't want to disturb the neighbors), then this probably won't work. Sound will get through that garage door pretty easily, even with panels on it. They will help a bit, but their main purpose is deadening the room's reflections--not stopping sound from getting out.
So ... you need to decide whether or not the door needs to be operational. If not, then seal it off with a wall just inside of it. That's what I did, and the difference in sound transmission was huge. Now I can crank up and not worry about the nieghbors hearing anything.
Are the outside walls of the garage brick or wood?
Also, regarding the AC, when we first finished it, the studio was much cooler than the garage part, but it still wasn't as cool as the house. So we closed some of the unimportant/unnecessary vents in the house (like bathrooms, utility room, etc.), and it helped a good bit. Now the studio is just about the same temp as the house. I installed a ceiling fan in there for good measure, and it feels great in there.
