Insulation of any kind will provide little sound reduction although it is useful in partitions and floors that have penetrations and cracks.

If the basement has concrete walls, the only point of sound abatement needed will be the floor above it. I recommend a drywall ceiling on resilient channels or even better: channels with acoustic isolation clips.

Agree with RES. You might want to locate the basement room that you want to soundproof below an area that doesn't have plumbing and has less foot traffic. It's difficult to keep impact noise on a hard floor from penetrating a wood-framed floor system. And I hope you have a legal second exit for any basement room you want to sleep in.

My brother has a home theater in the basement. Soundproofing was installed by a professional specialized company, but the sound from the films is still audible even on the second floor, especially the low frequencies. For sleep in silence there are downtimes cheap solution - ear plugs