Here's a general rule about insulation in an acoustical wall or ceiling application: Nothing works better than cheap fiberglass. You could spend big money on exotic insulation, but performance will not improve.
You could build a formidible wall between you and your neighbor, but the ceiling, floor, and two side walls could allow sound to pass AROUND your new wall. This is flanking: FlankingSoundproofing Company
The primary path betwen you and your neighbor is through that common wall, so treating it alone will bring some relief, but there will likely be a flanking issue that will ultimately define the results.