I do know that to effectively soundproof a room, there must be no transfer of sound vibration from one side of the wall to the other. Here's a system that I think is pretty DYI friendly, and inexpensive:
Using 2x6s for the sill and cap plates of the wall, use 2x4s for the wall studs. The difference is that you alternate the studs from one side of the 2x6 to the other (zig-zagging)on 12 inch centers. You'll have to set the 2x4s every 12 inches to have the appropriate spacing for attaching drywall on each side, but it won't take that many more to complete the wall than normal. Because the wall studs for one wall do not touch the surface of the other wall, the sound should not transfer as readily.
Of course, it will also help to add sound deadening insullation in the cavities. You might also consider a double-layer of drywall on the side of the wall where you're creating the noise, as this extra thickness will help to deaden it, too.
There are also some commercial systems available that attach to a regularly constructed stud wall which will allow you to space the drywall away from the studwall, thus keeping the transfer of those pesky sound vibrations from coming through the wall. I don't know how comparable it would be in cost to constructing the wall above with the 2x6s and the extra 2x4s.