For sound proofing (which keep in mind does not mean acoustically treating the finished room for great sound IN the room, but to help prevent sound from getting out of the room), you will want to make the area completely closed off.
Some basics are a room inside a room like mentioned. "Decouple" the walls and ceiling particularly so that sound doesn't get as easily transmitted between the inside of your theater and the rest of the house structure. This is not the cheapest by any means (read: it costs some bucks) since you can start getting into resilient clips, resilient channels, double layers of drywall with Green Glue (yeah, it is good stuff) between the layers. Insulation all around is good, and caulk "edges" (where the wall meets the floor, etc) with an acoustic caulk....
Don't forget to put in a floating floor to help prevent sound from traveling through and along the main house flooring.
Oh, and you can put a variety of rubberized "membranes" between a lot of different parts of this puzzle as well.
Use exterior grade steel doors to get in and out of the room, and make sure that they seal up nicely around the door frame.
Remove all solid metal air ducts and put in the rounded flexible stuff that looks like plastic wrapped insulation with a large spring holding the shape. Make sure that there are a couple of bends in it to help keep sound from shooting down a straight path in and out of the room. These are the nice things to use soffets inside the room for.
Whew. I am probably missing a lot there...
For the rest of the area where you want to keep sound somewhat contained, I would look at if some level of sound absorption would work OK instead of sound proofing. You could certainly insulate and decouple the ceiling to help with some of the direct sound transmitting through to upstairs, but to keep costs down, see if you can get away with plush carpets, furniture, etc instead and spend the money on the home theater area since those deep bass levels are going to need the most containment.
Get the plan for the main structure of the room(s) and then you can work on the sound treatments IN the room....
