Computers main purpose is not to reproduce music. They have horrid switch mode power supplies and plenty of electrical interference, which make it very hard for the audio system. In fact, just the fan-noise on some is enough to put some people off using them as serious audio devices. If you have good hearing you should notice an immediate difference between the output from a typical PC and a stand alone audio system.
The conventional wisdom is to bring the digital conversion and amplification out of the computer box. If you check out this forum, you will see plenty of advice on systems. These components will be optimised for music reproduction and delivering it to a wide range of headphones. Many give you extra features too, like swapping parts to tune the sound, balanced outputs. If your PC has a USB, SPDIF (optical or electrical), it allows you to get a digital signal, without interference out of the computer. Before you start laying out cash, back up a bit and check out what type of music files you have. You don't need golden ears to easily distinguish between low bit rate MP3 files and the higher bit-rates or lossless formats. The end result can only be good as the weakest link. Some headphones are very sensitive to the abilities of the amplifier.
If the unit is only going to sit on a desktop, you might look at DACs/AMPs with power supplies. If you might be mobile, there are a bevy of battery powered ones on the market too.
I'm at this juncture myself. I have just re-imported all my CD's into my mac using AIFF (lossless) coding and am waiting for the postman to bring me a portable headphone amp. For starters, I'll feed it off the dock line-out of a iPod classic but will then add a DAC (digital to analog converter) and run it from the computer's files for times when I'm sitting at my desk.
I'm then going to have to be patient since headphones, cables and electronics have a run-in time, over which the sound often becomes warmer and more coherent. I'll stick an old shuffle, loaded with FM noise and play it endlessly overnight for a few weeks. Hope this helps