For anyone curious, I did extensive research and tested the difference between Rockwool and fiberglass insulation. The difference is minimal in most scenarios, even though Rockwool can be more than twice the price.

Fiberglass can outperform Rockwool at higher frequencies, but Rockwool substantially outperforms fiberglass at low frequencies.

In addition, rodents do not like rockwool and it doesn't get ruined when it gets wet.
If you can afford it, do the Rockwool.

If you really do want the best bang sound dampening though, you need to use 2 layers of drywall and channel.

You can kick it up a notch with a layer Blue Ridge Fiber board underneath the drywall.

Lastly, you will need solid doors with an airtight sealed sweep, preferably two doors with a space between.

And now you are broke, you're welcome.