Homosote is the answer!
Well partly, it's a great soundproofing material. Cost is 25 to 30 bucks a 4x8 sheet, but you also need the metal strips that disconnect it from the 2x4's, then it's covered with drywall. Gets a little expensive, and I've only seen it at Menards, so if you don't live in the midwest it may be hard to find. It's also very dusty when it sawn. Anyway, that's my 2 cents. You could also use 2'x4'x 4 inch heavy insulation panels placed on the walls with about 1 to 2 inches away from the walls around the room in several spots. You'd need to cover them with something, my friend used some large garbage bags and then covered that with fabric made special for the panels. He found them on the web somewhere..
It's not too much work, depending on how many you make. He used them to surround a 412 while recording and you could hardly hear it all with a cranked Marshall. Then his basement flooded, ruining most of the panels, so he put them in his studio on the walls. Then, the AXE FX ULTRA came out and it was over.
and the Marshall and 412 were gone.
My advice, don't go too nuts with it and stay within your budget. Remember, nothing is forever. I insulated and soundproofed my garage and them suddenly had to move out when I was about 80% done! But then I found a new house, with cool neighbors
, (can't begin to tell ya how helpful that was) and a 20 by 22 room with a 15 foot peaked ceiling already finished. It was nice.
Aw geez I just realized there's two more pages I haven't read in this post! We men love our caves, and even more watching someone else build one and give them advice. It's kinda like barbecuing.
Good luck with everything Bman, and congrats on the new house.