When discussing soundproofing, it's easy to quickly go down the road of exotic (expensive) materials to help stop sound. After all, we like exotic materials and equipment, so this is natural. However, let's not forget that we can build a very well isolated room at a reasonable cost if you follow a basic, tried and true methodology.
#1 Decouple the framing. This can be done with staggered stud or double stud walls. To decouple the ceiling, consider clips&channel or resilient Channel (RC-1). Note that RC-1 attempts to decouple, however there is no industry standard or specification for its construction, so I’d be concerned about using it.
#2 Install absorption in the cavities. This means standard fiberglass or mineral fiber in the walls and ceiling. Know that there is no data (that I have ever seen) that supports that any other insulation (including the “acoustic” labeled, and recycled cotton) works better. Also, foam (open or closed cell) is superior for thermal, but distinctly worse for acoustic. Use the cheapest fluffy fiber you can find.
#3 Add mass. Nothing better than standard thick drywall (5/8"). Great mass at 70+ pounds a board, and generally cheap. Use two layers. Only mud and tape the final layer.
After that, you’d turn your attention to the ventilation, lights and doors. All of these are flanking paths for sound to get out of the formidable room you just built. They can be dealt with fairly easily, but you’ll want to design this in.
I hope someone finds this helpful.