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Like said. The main problem you will find will be due to sound bridges. That is where sound will travel through construction.
This can be solved by using cement board systems (like knauf here in EU) with aluminium profiles. You need to install them properly but all manufacturers of those systems having detailed instructions on their web sites.If you still have concern you can additional put another layer of foam isolation on wall. I found that piramide foam work great. I used one that is used for insulating motors on sailboats because is also fireproof.
Second concern you will have to solve is the door, intakes and outlets for vents and aircoold hoods. Silencer will help but you will still hear the sound of air traveling through hoses. That is so important that when you design room make sure that air hoses are as strait as possible since through corners or on long distance sound get stronger.
If you will use cement(gips) board it's easy to seal the room just by sealing joints of plates with silicon.
You don't need to build double walls if you use something like Auralex RC8 Reslilent Channel under your drywall. It only takes about a half inch more room.
I appreciate everyones help. I'm glad that I don't have to build a secondary wall. I'll take lots of pictures of the build. I probably won't start the build until the end of April or early May because I need to take a vacation to clear my head. Feel free to keep the ideas coming.