WHAT IS A GOOD QUALITY HEAVY DUTY INSULATION WITH SOUND PROOFING OR SHOULD AN ADDDITIONAL MATERIAL BE PURCHASED FOR EXTRA SOUND PROTECTION?

Have you looked into some good quality headphones? Just kidding. My tact would be to just staple some kraft faced fiberglass batt insulation into the joist spaces before I hung the drop ceiling. If you are really concerned you could nail a layer of sound board (brown and fiberous 4x8 sheet material) to the bottom of the joists before the drop ceiling. I have also heard of people drywalling the ceiling then using blown-in cellulose fiber insulation.

Do not use regular insulation. The Pink Panther makes insulation specifically for sound attenuation. Wait a minute.....Rap is not music......

Also remember that sound is due to vibration. The music is going to vibrate off every hard material that is in the room and continue bouncing until it finds an escape route. As Bob said, through the ductwork and door openings, etc. By the way, just ask one question at one topic so we can follow everybodys answer better and make fun of them easier. So.....the more soft accents that you have in the basement, the less sound vibration and the less frequent headaches you will receive. I have even seen people place carpeting up the walls in their loud rooms.