insulating basement ceiling

I have just finished framing my basement walls with 2x4s with a 1 inch gap against the concrete wall. Also, i stay in a townhouse and therefore I have 2 exterior facing walls and rest and all interior. In the past 2.5 years that i have stayed in this house the walls have been pretty much dry. Have a couple of questions about the insulation: 1. Do i need to insulate the interior walls? 2. If yes, then what kind of insulation do i need to use? Is it the same for exterior and interior walls? 3. Do i need to use vapor barrier ? And what kind? thanks

I'm in the planning phase of my basement finishing project and my question concerns where to put the vapor barriers on sound proofed walls. I live in an end unit townhome and I've read everything I can possibly read on sound proofing. I've decided to construct walls with a staggard stud configuration, 5/8" drywall on BOTH sides and insulation weaved in between the studs. I will be building three walls of this type of construction in an alcove portion of the basement, with only one of the walls being shared by my neighbor (so I don't think I'll have any moisture problems from the shared foundation wall.) That being said, where do I put the vapor barriers if both sides of my walls will be drywalled? The outer layer of drywall is more for vibration dampening purposes than anything else, but I wouldn't want moisture to build up there either. Would greenboard be of good use for the outer portion of this type of sound proofed wall? thanks in advance.