greenglue (or similar) + sheetrock. Also, you will need few inches of "empty space" between layers of sheetrock to really dampen the noise.
sound waves are very tricky at times so make sure you have no "sound leaks"
You project reminded me about Fitzcarraldo by Herzog starring Kinski. In short Fitzgerald wants to build opera house in the middle of Amazon jungle
there is also documentary about making Fitzcarraldo which is equally good or better then the movie itself.