The acoustic treatment that you make to your room (bass traps etc) will help a little.
The bulk of sound insulation/isolation treatment done to a room general involves preventing 'airborn' sound and 'impact' noise escaping (and entering).
This is usually acheived by sticking to the principle of MASS-AIR-MASS, for example building a 'room within a room.' The outer room is one layer/leaf of mass, the inner room is the other.
The airborn sound will be reduced by how HEAVY and how AIR TIGHT each leaf is and by increasing the SIZE OF THE AIR SPACE between the two rooms which should be insulated with ROCKWOOL.
The impact noise is reduced by physicaly ISOLATING the 2 rooms from each other as much as possible, so that the sound can not TRAVEL between the layers.
It will cost twice as much as you estimate and take five times as long.
Go to John L Sayer's forum for more headaches.
Good luck thumbsup