Basement and Foil-Faced Foam Insulation Help
Anything you do short of the whole resilient channel, sound attenuation blanket, sound board process will be an effort in futility. You will muffle the sound somewhat, but not kill it with regular insulation and/or foam board. The sound will travel through the fasteners connecting the drywall to your studs and/or joists. Sound proofing is possible, but costly.
If you can read this, thank a teacher. If you can read this in English, thank a soldier. Support our troops.