The op is asking about soundproofing materials, and for the space between the joists and behind the new ceiling I would 2nd the suggestion of Roxul Safe ’n’ Sound (instead of the more common fiberglass insulation such as Corning 703). Using the ASC isolation "channeling", to which the new sheet rock is attached instead of to the studs, will decrease the transmission of sound to the room above.
Applying the ASC Wall Damp to that sheetrock, with a second layer of sr on top of that, will decrease the walls ability to do what drum heads do when struck with a drum stick---move in and out in the middle, which is how they create sound. Sheetrock actually flexes between the locations where it is screwed down, the middle moving in and out, creating noise. Folkfreaks’s room exhibiting none of that---the room was very quiet. Not just in it’s isolation from the outside world, but in the sense of it not creating any sound of its own. The quietest room I’ve ever not heard ;-) .