You can double up on fiberglass insulation for an increase in sound proofing, but at the expense of R value. Probably the best way to do it is to use the spray on foam stuff. One of those renovation shows on PBS did it to a house and it was super neat. You put up dyrwall on one side of the studs along with all of the plumbing/wiring, then spray the stuff on the other side. Once it expands, you use a rasp thingy to cut it down to being level with the studs.
When it comes to between floor joists, there is supposed to be an airgap between floors. A drop ceiling would definitely take car of this. You could then put some sort of sound insulation directly onto the gyp board attached to the floor joists.
There are quite a few guides to soundproofing on the net. It really comes down to how much you want to spend, and the exact conditions of your setup.