It might help cool the situation and help the OP understand why ABSORBENT material will not help to give the physical reasons?
Although he wants to prevent sound getting out, any 'treatment' he does will be just as effective on sound ingress.
Take a bare, reverberant room and put in a goodly amount of absorbent (GR, RW, duvets!) The sound level exiting the room will drop. BUT SO WILL THE LEVEL INSIDE THE ROOM! Net result? You 'gain' precious little. It is quite obvious that if you could absorb ALL the sound in the room you would never bother folks!
Sound must be stopped by 'mass' p'board, better brick walls...But! Even a tiny leak, 25mm hole will allow the transmission of as much sound as a 50ft* solid wall so all has to be airtight. Then, any connections, cables, ducts etc must be compliant so as not to transmit sound and last of all is mounting the whole room on a compliant base.
I think it can be seen that doing the above is going to be very expensive and impractical unless you have a very large space to begin with.
Them's are the 'facts' as I recall them. Now, kiss and make up FFS!
*I might have that dimm' wrong but the concept is valid
Dave.