owens corning r-13 will be good for what you're planning. you don't want facing. hanging it would probably be annoying at that depth. you can stack it but if you stack too many layers on top of each other it will compress and be less effective. i have done what you are describing and the way i did it was by attaching shelves to my wall at 2' intervals, then stacking the insulation on each shelf. after you've made the trap, you're going to want to cover it in fabric. i suspended a curtain from my ceiling, but you could also build a frame and staple the fabric to it. i used a layer of cotton and a layer of cotton batting to make sure no fibers would escape.

some good inspiration here, look for the albums that show the studio construction process: https://www.facebook.com/MyRoom.Acoustics/photos_albums