Insulating a garden building.

I've a 5m x 3m garden building (really swanky shed) that I want to use as an "outside room" for various purposes including music practice (no electric instruments). I want to insulate it for heat and sound. The building is new, with shiplap cladding on 75mmx38mm members. What might the best insulation be? I've considered Jablite, compressed rockwool (expensive), glassfibre... that would be OK for heat, but what about sound? Would puting plasterboard on the inside walls be helpful? The finish inside is to be T&G matching, so I need to be able to affix this easily to (whatever). Any helpful ideas will be much appreciated!