Use fiberglass sound batts in the walls and ceiling to start with. If you can do a suspended ceiling in the room and insulate on top of the ceiling panels it will even work even better because the sound will not be transmitted through the wood floor joists.

Thank you for asking this. My girl and I just bought a new condo. It has an unfinished basement(yes) and I would like to build a room that is soundproofed from outside noise.