If you're seriously going to build, keep this premise in mind:
The only thing that stops sound is MASS. Lots and lots of it. No other trick will work, no shortcut exists around the laws of physics. So the underground idea is pretty much right on, unless you put some massive effort and/or serious $$$ into an above-ground Fortress of Rockitude.
If you dig around on the internet (pardon the pun), you'll quickly see the difference between what most people call "soundproofing" and really doing the job. Egg crates and blankets and foam -- that's all sound treatment. It's not soundproofing. It'll help tame bad high-end reflections in your room, and make it more dead sounding inside, but it doesn't do jack squat about actually stopping sound. And there's just an amazing amount of sound involved in any live music situation, such that it's very hard to truly reduce it to nothing.
Actual soundproofing requires things like floating/double walls, floors, & ceilings; vestibules for any/all doors in or out; special double-paned windows; treatments for ventilation systems; accoustical caulk for all drywall/wood joints, etc. It's work, or it's money, or it's both, so be prepared.
Check this site out:
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Aside from the horrible HTML design, it's a very informative site, which should help you form an idea of what you really want to do.