*To keep much of the sound down, put spacers (ie firring strips) between the studs and the wallboard. That will reduce the surface area of contact points in the walls, which will reduce the ability for vibrations to travel through them. (This will help with low-frequency sound.)
*The more surface area INSIDE the room, the better. (sort of) what that means is... acoustical tiles work by absorbing the high frequency sound waves. A smooth-as-glass surface will not absorb much, but a piece of foam will absorb alot - especially if the cavities in the foam are smaller (smaller holes means more holes per square inch, which means more surface area to absorb waves.) And corrugated foam has even more surface area, so it does a better job. (This will help with higher-frequency sounds.)
See if you can find a book at the library. There are some great books at my public library on skilled trades. The older books are especially helpful because they are low-tech.