I would consider isolating the room from the rest of the house (and neighbors). I used Kinetics Noise Control IsoMax clips to suspend (float) walls and ceilings in my media room (basement room, concrete floor). See
https://kineticsnoise.com/isomax/sound-isolation-clips.html I had the builder use double-drywall panels, glued and staggered so the seams did not align, all seams/joints caulked, and all installed on the clips to reduce noise to the rest of the house. Outlets and light boxes were backed with caulk to reduce sound through them. A minisplit HVAC unit is used so there is no ducting to the rest of the house, with baffled inlet and a quiet fan in a ceiling vent for exhaust to get airflow into and out of the room.
The door is a heavy solid-core exterior door with full weather sealing to reduce sound transmission through the door. Provides most of the benefit of a studio door at much lower cost.
For outlets, I ran 20-A lines to the front wall where all the equipment lives, and a 15 A loop around the rest with several outlets split so the top is controlled by a wall switch as you enter and bottom always on. That way I can use floor or table lamps instead of in-ceiling or overheads to reduce the number of holes in the drywall. I do have one high wall sconce for ambient lighting when we watch movies. I do wish I had run another 20-A line at the back for the rear subs but have not had any problems.
I am not a fan of in-wall wiring; it always ends up just a little off where I need it, but if you do route to a convenient place with wall panels you can plug into. That way you have short runs to speakers (or whatever) from local wall plates for a cleaner look.
Don't forget an Ethernet run or two if desired.
HTH - Don