Really it comes down to your PC (or laptop) and headphones. I have head computers with dead silent outputs (MAC) or ones with audible power supply whine. The other issue I have run into is inability to drive cleanly at high volume though it may be pretty good at low volume. External DACs have better amplifiers that will drive a variety of headphones cleanly at full volume. You don't have to spend a fortune to get an DAC-amplifier that is about as clean as you could ever hope for. You could spend more, but then you are paying for a brutally over priced tone control. There are better ways to spend your money (like on better headphones).
What I learned, and I cannot emphasize this enough, is that you must learn how to equalize your headphones. I went through some expensive headphones never quite happy till I discovered that the frequency response of most headphones, even expensive ones, can be rather poor. It's not something they tell you when you buy them. There are some good resources on the web with headphone reviews with frequency response on something the resembles a human head. They will give you a give starting point.