Actually, this is a tough one. I can only think of one word. COMPROMISE.
Soundproofing is a misnomer. There is no such thing. The proper word is TRANSMISSION LOSS, which is how much sound makes it through the envelope assemblies vs how loud it is outside of it. Transmission Loss is rated in DB. Assemblys such as a studwall are tested in labratorys and are RATED according to how much sound is TRANSMITTED. Like this:
The question is defining how much do you need . If you can't define your compromise point, then you can't define what you need. Heres a few considrations as well.
Loss of space is proportional to Low frequency Transmission Loss goal
Trapped Low frequency within requires low frequency absorption which also causes loss of space.
Low frequency rumble(structural transmission) from the street may be difficult if not impossible to prevent on this budget. Even with a large budget, and a larger room. Short of floating a room within a room, or other decoupling methodologys such as resiliant channel or Risc isolators, mass is your only option. Add layers of drywall untill structural failure or your isolation goals are met
Ha! Just kidding However, there is a limit of diminishing returns using mass alone. The limit in this case is space. Possably the floor structure above
as well. I know of builders who utilize 5 or more layers of drywall in a small room to prevent 110 db transmission
This is the reality.
Use of Resiliant Channel requires venting or removal of drywall leaf in proposed room prior to installing the RC. Up to two layers of 5/8"drywall can be fastened to RC. Many decoupling and fabrication details to address.
If you have a hollow core door, change it to a solid core. Install door seals, thresholds, , insulation in all walls, caulking or gasketing electrical outlets and lighting fixtures, pipes and all other flanking pathways.
HVAC or ventilation is required in a sealed envelope. However, ducting connected to other rooms can be a flanking path for airborn noise transmission to and from the studio.
For the open cieling, assuming the floor sturctural framing is up to code, adding 2 layers of drywall(5/8")directly to the underside of the subfloor, between the floor joists will help. Usually by adhesive/screws and or cleats/screws. Then caulk ALL joints, pipes, ducts, etc. Remember, this becomes added mass to the floor LEAF. That makes it important to NOT trap air or create an airgap between this mass and the subfloor. Once insulation is installed between the floor joists, use 2 layers of drywall with staggered and caulked joints. This becomes the SECOND leaf. This leaf may be fastened directly to the joists, or Resiliant channel may be used, but that is determined by your goal. If structure born noise such as foot patter is a problem, or you want to play loud at two in the morning, RC is definetly in the picture
Well, I'm out of time. Hope this helps some.
Here is a cieling detail with a double wall.