Adding insulation underneath the paneling would be a good start. I think that fiberglass bats (Owens Corning sells some specifically for soundproofing) would probably have about the same effect as foam or soundboard. This will cut down on midrange & some high frequency noise.
As long as you have the paneling off, you might gain some soundproofing by attaching horizontal furring strips (1x2) to the studs. That would reduce the area of contact between the panel (which absorbs sound) and the wall itself. This will cut down on low frequency noise (bass.)
You could fill in between the furring strips with 3/4" foamboard also (or any other rigid soundproofing material.) The important thing is to make sure it is fire-rated and doesn't give off toxic gas when it burns. As long as the drywall and paneling are fire-rated, it should be OK. (Chances are, paneling is NOT fire-rated.)
You can add fiberglass bats in the ceiling too - although the noise you usually get through ceilings is low-frequency - so you will probably still have some noise even after installing insulation.
You can insulate the pipes by putting foam pipe wraps on them. More importantly, fill in the holes where the pipes enter the room. A can of spray-foam or some fiberglass insulation would work.