Oh Brian, I wish you luck in this venture. I understand the troubles of the noise next door. I too had the same exact problem and posted here to get info.
heres a link that might help. http://www.soundproofing101.com/soundproofing_2.htm
Heres what I ended up doing and regreting it.
Took down existing drywall. Found out there was already an older soundproof board there. Took that down. While having bare studs there I ran a few more cable/phone and outlets on that wall. No insulation there so I filled up the bays with R-13 I think. I squeezed caulk onto the stud as recommended to reduce vibrations. I screwed new soundproof board from home depot onto studs. I installed 5/8 drywall on top of it. I plastered, taped, sanded, painted.
I STILL HEAR NOISE!!!! THAT IS WHAT I REGRET.
I WISH I WENT THE OTHER ROUTE. BUILDING A NEW WALL IN FRONT OF THE EXISTING WITHOUT TOUCHING IT. IF YOU HAVE ROOM DO THAT!