The foil insulation is designed to work with an air gap. Read the instructions carefuly. If you use foil, put it on the back of whatever you use to build the walls. If you use foam board, just cut it and shove it into the gap created by the wall ribs.
Neither the foil nor the foam insulation does much for noise. You need some kind fo mass damping material applied to the walls and floor to deaden sound. fatmat etc... just find something close to you and in your buget. Apply the mass damping material as per the instructios that come with the material then build your walls and insulate according to whichever style of insulation you choose.
