If the only input you have on the music system is analog then that is the best you can do for sound.
Use the DVI connection from the PC to the monitor. That is the best you can do for picture.
For improvements in audio you can upgrade the music system to one with a USB DAC built in so you can connect it to the PC with USB and bypass the PC audio. You can also get a separate USB DAC and connect it's output to the Sony. The Sony and the quality of your music files will be the limiting factor then.
For improvements in video you can upgrade the monitor. DVI and HDMI are the same quality but if you upgrade to a 4k monitor your PC has to be able to output in 4k. That might require a video card or new motherboard.