The green rocksol or rockwul insulation is rated for fire and hhas a good sound blocking ability when installed correctly.
a 1/2 drywall ceiling can be strapped with resiliant chanel to absorb noise ( not nessesarily a do it yourself project but can be done with help and a little care).
an insulated accoustical tile can used Bailies or Armstrong could give you info on thiers they are both good systems