I'm nearing completion of my project (one day...
) and soundproofed the walls adjacent to our living space and have done extensive research. If you are going to do it, you have to cover all the bases or sound will seep through. Not mentioned in the thread: electrical outlets, switches and any wall penetrations. Sound will leak right through them. Putty pads help.
It's a costly and intensive effort, but well worth doing when done correctly. As mentioned, staggering the walls will result in a much greater degree of soundproofing, but this may not be possible. Double drywall and greenglue is also very effective, as mass is a serious sound dampener. You could double drywall both sides of the room (inside the room and outside the room on adjacent walls and ceilings).
Or if you have one room from which the noise will eminate (i.e., home theater), you could consider soundproofing that space instead.
But wherever you can stagger a wall (or better, build a separate wall, but be aware of the "triple leaf effect") or use resilient channel for the ceiling below, all the better.
This link has a lot of articles that will educate:
You can also google the terms: Soundproofing, staggered wall, STC rating.