My opinion is that if you want to get a little more serious about audio for your PC, you would also need to get an external DAC/AMP with SPDIF interface. There are such units out there that would connect via USB.
From here, get yourself a decent set of open back headphones... don't go cheap. Here are two models to consider.
Beyerdynamic DT990: http://www.amazon.com/Beyerdynamic-DT-990-Pro-250-Professional-Acoustically-Applications/dp/B0011UB9CQ
Sennheiser HT650: http://www.amazon.com/Sennheiser-9969-HD-650-Headphones/dp/B00018MSNI/
I recently got the HT650s and I love them!
Here is where the amp comes in; these headphones have higher impedance, so they need the amp to drive them, then the DAC to convert the digital audio to analog for you. For instance, the DT990 comes in a 250 ohm and 600 ohm variety, so you would look for an amp that can drive that amount accordingly.
Me personally, I went with the Fiio E17 / E09 combination, which works fine for my setup. The E17 is also portable, so I would have the option to use it on the go if needed.