As soon as you attach your wall studs to the ceiling (floor) joists above, you will have
sound transmission going in both directions. If you want sound isolation, you need to keep
the walls free-floating from the rest of the house, and build an isolated ceiling
structure as well. (room-within-a-room)
All 4 walls and the ceiling need to be
independent for sound isolation.
I also second the comment that you should
consider 2 layers of 5/8" sheetrock.
"Never interrupt your enemy when he is making a mistake"