Soundproofing

No problem. Simply build it inside the existing one.

Next?

He's kinda right.  Soft batting between studs, joists will do very little.  You need mass that ideally is separated from mass.  Then find a very heavy solid door sealed on the perimeter.  And then be able to block sound that travels in air ducts.

micthurst 

Do you have a high basement unfinished ceiling at present? When we had our house built I knew I wanted a basement listening room so I had the builder put in an extra course of concrete block to allow for a reasonable height for my listening room.  I have an insulated drop  7'6" ceiling.  As it is, you can hear little sound above in our dining room.  One thing I did was I decoupled the speakers and subwoofers from the room. The subs used to rock the upstairs but the decoupling was magic! in that regard. My family members say that they hear music coming to the upstairs via the heat/AC metal ductwork but only to the extent that they know I am down listening.
I think the drop ceiling is key as the sound is not vibrating through the wallboard to the upstairs floor joists.  By their nature the ceiling tiles absorb sound.

I agree that mass and decoupling are the keys. ASC, among other acoustics firms, can provide guidance; they sell products for this. There are many other online outfits who might be helpful; this is one. Another firm that specializes in audio is Acoustic Frontiers. No matter who advises you, really good soundproofing will be expensive.

Near-complete isolation can be difficult to accomplish in any case, and particularly in a basement while maintaining sufficient ceiling height. My basement room has some sound leakage through the ceiling, but to get more isolation would have meant reducing the 7-ft ceiling height further; it’s already lower than ideal.

I suggest you avoid installing any lighting in the ceiling -- use floor lamps instead. Any penetration of the ceiling -- or the walls -- is a path for sound to travel.

Good luck, and have fun!