I should probably even apologize for saying anything, but the subject of good audio from my PC has become my new passion. This is probably way beyond what you were thinking of spending... but for around 410 Dollars you go here...
https://drop.com/home
You get a Sennheiser HD 6XX... 220 Dollars
You get a Massdrop Grace Design Standard DAC ... 95 Dollars
You get a Drop O2 Headphone Amplifier... 95 Dollars.
Looking at the reviews / comments at drop.com ... most people that do that are happily shocked by what a super great sound they get.
410 is way more than you want to spend, I guess, but that’s what it would cost for a super great sound.
Oh, and Drop has an odd way of doing things. They wait until they have enough customers, then they send the order to Sennheiser. So figure a two month wait. But the HD 6XX headphones are widely respected by everyone that knows. Very good reviews.