First of all, it should be mentioned that the insulation process needs to be done during the construction process of the house, otherwise you would have to either tear down parts of the wall to be able to insulate it or add a second wall.
To ensure that you keep sound from space, it is necessary to block it and not absorb it. Sound absorption can only do just that.
Installing drywall is one of the most straightforward ways of adding more mass to the wall, effectively adding an additional barrier that prevents sound from getting through.
One sheet of drywall will provide you with a significant reduction in noise, but the best way to go about it is to install two layers of 5/8 drywall.
Additionally, you should weigh putting a noise-proofing compound between the two layers, which will make a slight air pocket to further increase the insulation.
Doing this should give you an approximate STC of 35 or 40. In other words, it will reduce the noise that’s allowed through the wall by about 35dB-40dB, which means that loud speech, for example, will be audible but unintelligible.