There are much more knowledgeable people here than I, but here is my two cents. Normally you install 30# roofing felt under 3/4" hardwood flooring, I would replace that with a sound deadening vaper barrier mat (there are some made for laminate floors). Insulate the basement ceiling with rockwool insulation and use 5/8" Type X drywall on the ceiling of the basement. It's not going to be perfect, especially with hard soled shoes, hi heels, etc, but it is a start.
7.1.4 Theater Room (In Progress): JVC-RS46U, Silver Ticket AT 2.35:1 142”, Onkyo RZ830, Anthem PVA-7, Panasonic DBT-110, JBL Studio 270’s, 4 - 15" DIY Sealed Subs
3.1 Living Room: Samsung 64” F8500 Plasma, Anthem MRX 300, Dynaudio Audience 52’s, Dynaudio Audience 122C, NHT SubOne