Yeah, you are going to have to spend some time thinking about soundproofing. Staggered studs, clips and channel, double drywall and green glue, there are lots of methods that achieve varied results. However with any method you choose, any hole in your drywall will be a weak point to transmit sound. So outlets need to have putty pads, light need to have backer boxes, doors need to be completely sealed. And the reason I asked is because your projector room will also need to be sealed up. If it's outside the theater, sound could enter/leave the theater through the port hole or any other opening. It's quite a complex subject and you should have a good plan in place before you start construction.
Nothing in this world will tick you off more than seeing a vegetarian eating pudding.