Have your contractor do the interior walls of the room with "2x6 staggered stud" construction. He should know what that is. Then, have insulation woven between the studs. That's a good start.
You may also consider using "resilient channel" or "hat channel" (same thing) in order to "hang" the wall off the studs. You can get it at Home Despot too. It reduces sound vibrations from coming through the walls. Works great. If you already have 2x4 walls, I'd definitely do the resilient channel.
Check into using "Homasote" a man made paper material in 4x8 sheets from Home Depot. It goes up like drywall, but weighs only about 1/3 as much. Put that on prior to drywall. I found it did a great job at blocking noise.
Be sure to close any openings, i.e. holes around outlets, etc. since these are leaks for sound to travel through.
Or you can do double layers of drywall, having the sheets put on perpendicular to each other so joints don't line up. Don't forget to treat ceilings too!
Plan out your wiring well, since it'll be harder to access later (i.e. fishing new wiring).
Wire the room for HT use whether or not you will use it for that. Down the road you may change your mind, and it will make the dedicated room more appealing if you sell.
Putting plenty of effort into sound diminishing rooms pays off handsomely. I built 7.5" thick walls for my HT (in basement) and the washer and dryer in the utility room ten feet away almost cannot be heard at all. My walls are (from interior to exterior) .5" sheet rock, 2x6 staggered stud walls with insulation, .5" double leg resilient channel, .5" Homasote sheeting, and .5" sheet rock.
Don't forget, you'll need special order solid core door for such room; when I looked, the largest single piece door jamb was 7.5" width. I originally wanted an 8" wall, but changed it to accomodate the door jamb limitations.
"Room Tuning" is the term for adjusting the sound of components within the room. Also well worth pursuing. But, it's kind of sad to build a room wrong (without sound proofing) then treat it all nicely in interior and have intrusions through the walls from the outside.
If you do the room well enough, it will seem as though you have stepped into another building when you enter it. People often comment on how quiet my HT is, since no sound intrudes from the rest of the house. It is acoustically a separate building. That should be your goal, and you have the golden opportunity to do it now that the walls/ceiling are not done.
Also for serious consideration: if you are handy (even if you're not - I had never built anything prior to my HT) and have the spare time, consider the contractor not finishing the room, but you doing it. Headaches? Yes, but the one luxury you get doing it yourself is TIME; time to consider logistics, electrical plan for lighting, outlets, etc. Time for considering where to place components, i.e. in wall, or under screen. Time to pick sconces, wall finishings, etc. Time to insulate well, not quickly. Time to caulk openings and consider if you can build a sound proof ceiling. Time to consider entrance to room, where the surrounds will be and wire for them, etc.
This is all situational. Anything you do to soundproof will be well rewarded as the room is used.