You could insulate floor with fiberglass batts and put up a drop (acoustical) ceiling (if the basement space is to be finished), or you could use special sound absorbing insulation and drywall the ceiling - be careful around the furnace as you probably need fire code stuff, i.e.; not sound board/homosote but at least 5/8" fire grade drywall, if not two layers.
As for soundproofing I have used resillient channel with good effect. You mount this across the joists with isolating padding in between. Also make sure to seal ALL drywall joints with acoustic calking (not regular calking) before joint compound. This means ceiling/wall joint, and calk all joints where sheets meet each other before drywall tape/mesh. See: http://www.soundproofing.org/infopages/channel.htm