I'm starting Duke3D and I get sound stuttering and graininess (not the grainy that's already there because of the game being from 1996). It works but isn't pleasant. I tried lowering the mixing rate to 11Khz but nope.
Also, music seems to work but the volume is very low despite maximized music volume ingame and max MIDI volume in windows.

Sound issues for me too, but different. 90% of the time when I start the game the sound FX don't work but music does. I restart the game and then the FX work too.

Try using VDMSound.

Or try it with eDuke32

try playing with the prebuffer and blocksize parameters in the configuration file of dosbox.
(the file is called dosboxXXXXXXXX.conf)
where XXXXXXXXX depends on the game. Probably DUKE.

You do not need VDMSound when using DOSBox. DOSBox incorporates all VDMSound functionality.