Honestly, something like the Sennheiser HD 58X or HD 6XX would be a great starting point. Those headphones get recommended a lot for a reason; they serve as a great reference and teach you a lot of things about what a good audiophile set of headphones should do for you. Also, as your system grows, those headphones will scale up with you. They really do scale like mad with better gear.
If you want something that will have more treble sparkle and "air" get the AKG K7XX or the Hifiman HE-4XX. Personally I don't really use my K7XX much because it's not to my taste, but your experience may differ.
Whatever you do, don't get the HE-4XX unless you plan on getting an external amp. Heck, for that matter all of the above mentioned headphones benefit from an external amp and better DAC. Out of a PC, even with some expensive Asus soundcard you're only going to get about 60% of the performance of these headphones (less for the Sennheisers; those scale all the way up with gear that costs in the thousands).
Everyone starts somewhere. Good luck, have fun!