Here's an article describing room within a room construction: http://www.soundproofingcompany.com/...within_a_room/
The second wall would provide the decoupling, rather than the clips.
Regarding the cement board, you could do that, however the cement board is simply more mass. I'd stick with drywall as it's easier, faster and cheaper.
I'd leave the garage floor alone, as it is already massive.