Standing on Soap Box with megaphone:
Anything more involved or expensive than the cheapest R-19 (6") fiberglass you can find isn't going to give you a real benefit. Way too much benefit is tied to insulation. Why? Because it's intuitive that insulation should work. It does work, obviously, but only to a point in practical terms.
But it doesn't take much insulation to provide absorption in a cavity. That's where people get hung up. You don't need thicker than 6", but you can if you want, certainly. You don't need anything beyond cheap fiberglass, but you can if you want, certainly.
Save your money and invest in other aspects that will really give you gains. Like decoupling, mass (extra drywall) and damping.
Combining these elements will certainly provide more isolation. Don't blow the whole budget on just the insulation.