Hi, Corrie. There really is not much need to even think about insulating interior walls unless you have a 16 year old with a drum set or something. Even then, just adding fiberglass insulation will not do that much without other measures. If you do expect to have problems with something like that, I suggest that you check out a product called Homasoat. Putting a layer of this under the drywall will do more for noise reduction than the fiberglass and both will do even more.
But for normal conditions, no insulation is needed and the drawback is cost.