You should use what the manufacturer recommends for soundproofing. A thicker insulation will not provide considerably more soundproofing - it will just cost more. Soundproofing of high frequencies is done by deflection and absorption of sound waves. So airspace as well as surface area are important for soundproofing. Insulation will help control sound - but will do very little to control low frequency soundwaves. You need a material to interrupt the waves as they vibrate through solid materials (drywall, studs, ceiling). Rigid foam insulation betweenthe studs and the wallboard would work, also the "u-shaped strips" described below would help. You can use 1x2 furring strips instead of the u-strips, although they won't be quite as effective. (Mounted across the studs, beneath the wallboard.)
(The "staggered wall" described below wouldn't be too practical in the basement.)
This comes from Owens-Corning: " To cut down on noise -- a boon when mom or dad works at home and summer vacation-crazed kids are stampeding through the house, Owens Corning suggests QuietZone acoustic batting. They can't soundproof, but they can diminish sound considerably. The rolls of batting are made to fit between the studs of standard 2-by-4 framed walls.
For even more sound control, Strauss suggests adding U-shaped metal strips called resilient channels to interior wall construction or across the floor or ceiling joists. The resilient channels keep drywall separated from wall studs or joists to break up a sound's vibration path. These are available from most drywall contractors.
(Another way to increase sound control is by building interior walls with staggered wall studs set varying distances apart. These staggered studs also interrupt the vibration path to prevent sound from spreading. Solid wood doors help, too.) "