New
#21
Blue port on the monitor is input for sound so to have any chance of getting (if there are speakers in monitor) analog sound from computer is to connect it to green output on computer.
Blue (on monitor) > Green (on computer). Green connector on the monitor is pass thru to connect some external speaker or headphones to it.
As for VGA vs. DVI, apart from possibility to let sound thru is that less possible interference to signal and ability to use much longer cable. DVI could also be used to convertto HDMI or display port while VGA would need an active converter.