there's always
Auralex Acoustics 101 to help keep you busy while John's site gets transferred.
Really good info in that document.
It's hard to come up with a "best way" solution for what you want to do. There's a lot of variables that will affect what you can/will do. Your budget being the primary variable.
What's the exterior structure like that you want to build this room in? Basement? Shed? nuclear bunker? that would be cool
One possible plan could include installing drywall/plywood on all exterior walls, caulking and sealing all of those walls so they're airtight.
Then building your stud walls and a suspended ceiling that is physically isolated from the exterior structure. Same with the floor. You want to remove as much vibration to the exterior structure as possible. Then you want to also caulk and seal the interior structure so it is also airtight.
Then, since, all sound will be contained in this small room, you definitely want to control the sound waves in it .... this involves installing insulation, foam, building slot resonators, bass traps, etc etc etc. There's LOTS of options here. And this is the trickiest thing to do, IMO.
Of course, you need to consider all electrical and ventilation stuff too ... audio cables & connex, outlets, etc etc.
That's a very minimal summary of what's involved. What's it gonna cost? Well, it depends ... I spent about $6k on my studio space about 4 yrs ago (2 13'x15' rooms ... and NO acoustic control stuff ... yet). For what I accomplished ... I think I spent too much ... but I learned a lot so it comes out even, I guess.
My advice is to learn as much as possible now before you do anything. Also, get a plan early and stick to it ... this can be a pretty big money pit if you don't have something to keep you on track. Definitely check out John's manual when it gets back online. I liked his writing style much better than the Auralex stuff.
Good luck!