Advice on dedicated room

You can take a look at my system in my house of stereo. It includes construction pics and details in the comments section that may be helpful to you. Have fun with the process. Be patient.

Home builder for 35 yrs.. 2x4 studs with closed cell foam on exterior walls. Open cell in ceiling. This is what I do in basements here in the Midwest to control temp and sound through the ceiling to first floor. Good luck. 

@baylinor and @mickeyb 

Thank you for the advice. I’ve received a lot of great input from everyone.  
@mickeyb 

Does the closed cell foam go between drywall and stud or in the space between the studs? 

Sound insulation behind a drywall will essentially do nothing for the room acoustics. It will make elsewhere in the house quieter. If that is your aim then good. Double thickness drywall will help a little inside the room, ensure the two surfaces are very well glued together and very well attached to studs. I have smaller room than this with 45 degree corners, that seems to help a little. Remember sound doesn't know what size the room is it is purely a mechanical acoustic response to the whole environment i.e. furniture, carpets, surfaces (hard / soft), angles etc. There are three aspects reflection, absorption and diffusion. You usually have a mix but rarely the right mix. Carpet the floor maybe plus rugs, the ceiling is a big flat space, and reflective but quite a way away. Some diffusion is good, two ceiling fans perhaps? I have a very large recliner in soft material and its effect is dramatic. Other softer material seats help and I have built some prototype bass traps that diffuse, absorb and use membranes, they do work but are difficult to get right. 

room modes online calculators abound…note that they don’t include a non parallel wall…hint, frame that in now. Also you want low noise in the room, so insulation will improve the sound. S/n is important. 

Jim Smiths book is great - Getting Better Sound.