It will depend on what you want. You won't get the most out of your music with a gaming headset, though I have heard that the PC320 is not a terrible choice.
A DAC and Amp that is separate from your computer will at least marginally improve the clarity of your music, as it will remove the music processing from the electrically noisy environment that is all PC cases. You may not hear the interference, but it is there at some level.
That said, your largest improvement in music quality may come from some dedicated music headphones. One potential issue I see here is the fact that your Xonar DS does not have a built in headphone amplifier. That's not to say that you won't get enjoyment out of a pair of headphones that would normally be run with one; but you won't get the full experience of the headphones and may be left feeling that a very good pair of headphones aren't worth it (when they are if driven properly).
On the headphone front, are you looking for open (wider soundstage, leaks sound in both directions) or closed (smaller perceived soundstage, greater bass impact but bass could bleed into mids, noise isolation) headphones? There are some good options, both that benefit from an amp and that don't necessarily need one, in your price range, but narrowing it down to a type would likely help those recommendations.