This topic comes up from time to time here on HRT, and I thought this may be of interest to some. You can build a very well isolated room at a reasonable cost if you follow the following 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. Resilient Channel (RC-1) attempts to decouple, however there is no industry standard or specification for its construction, so Id be concerned about using it.
#2 Install absorption in the cavities. This means standard fiberglass R13 in the walls, R19 in the ceiling. Know that there is no data 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 fiberglass you can find.
#3 Add mass. Nothing better than standard 5/8 TypeX. Great mass at 70+ pounds a board, and cheap at $7 a sheet. Use two layers. Only mud and tape the final layer.
#4 Consider damping these drywall panels with one of several field-applied damping compounds. Some work better than others, and independent lab data shows you get what you pay for here.
After that, youd 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 youll want to design this in.