One solution that would work the best in your situation would be a room within a room approach. Use existing concrete where available for floors walls because it doesn't transmit sound very well. Every where else, build a wall and a false ceiling that are disconnected from the remainder of the structure.
Become familiar with the products that The Soundproofing Company has. Then contact them and explain your situation. I would plan for installing a long term home theater building on the framework that you are installing now, so as to not waste this effort.
They have clips that you can use to connect the ceiling of the soundproof room to the floor above. These clips will help isolate the sound in the room below, by not passing on vibrations. For the other walls, you can either build a double wall where they don't touch with insulation in them. One wall is the theater room wall, the other wall is what you see from outside this room. Drywall on only the visible portions. You can also build a slightly less effective wall by using 2x6's and stagger the 2x4 studs so that they support drywall, but they don't touch each other. Use a solid core door that seals good all around. Use 2 layers of drywall seperated by Green Glue, which is sound dampening. etc etc etc. Sound proofing is a science that is fairly easy to learn.
