There are four elements to soundproofing; decoupling, insulation, mass, and damping. Mass is covered by two layers of drywall, insulation should be pink fluffy fiberglass insulation, and Green Glue is the damping agent. Decoupling provides a physical separation between both sides of your walls and ceiling. Sound likes to travel through solid surfaces by vibrations, so by splitting up the connection between two sides of a wall you remove that path.
All four of the elements of soundproofing work best when employed together. Decoupling really only requires some extra 2x4s for double walls and isolation clips and channel for the ceiling. Depending on the size of your room and which clips you buy, it won't add much to the cost; perhaps a few hundred dollars, which is well worth the investment for increased performance.
Give Ted and John a call at The Soundproofing Company. They'll treat you right and help you make a plan for your budget.