Droff,
If you are talking about a bonus room that is in the attic above your bedrooms, you might want to reconsider your willingness to accept noise throughput the house. You will get a significant amount of sound being transmitted to the lower levels -- especially the level just below the room.
Most folks break their discussion of sound treatment done into two categories -- sound isolation (i.e., sound entering or leaving the room) and Acoustics (e.g., improving the quality of the sound inside the room by addressing the issue of sound reflection). Scott was suggesting that you would get better sound isolation if you use double dry wall with a damping material like GreenGlue. You should check out the GreenGlue site it is loaded with information (
www.greenglue.org). The incremental cost of double dry wall and GG is worth it. It will cost you much more to fix the noise problem later.
Also, if I'm correct and your bonus room is upstairs over the bedrooms, you should really consider isolating the floor. This will not only reduce the low frequence (i.e., bass) noise that will transmit down into the bedrooms it will also reduce the noise from foot traffic upstairs. I have four kids and I can tell your from personal experince they will create a lot of noise while playing their video games. This will be the last thing that you want to hear on Saturday morning when you and the wife are trying to sleep in.
Regarding the sound quality in the room. This is contolled by using different types of acoustical panels that absorb or diffuse the sound. These are installed at different locations in the room depending on they desired sound treatment. There are several good articles and posts on this site that discuss various ways to accustically treat a room, you should look at those postings and articles. I have not heard of anyone recommending the installation of sheetrook over plywood as a means of improving the accustical sound quality in the room.
Save you money on the plywood and do the double drywall with GG instead.
After the room is constructed you can buy (or make) a few accustical panels that will hang on the walls which will improve the room accoustics. These panels are not expensive -- especially if you make them yourself. The big issue is the proper placement of the panels.
Good Luck