Well I personally have the Xonar Essence STX with Beyerdynamic DT770s and I find the sound quality amazing.
If you're new to 'audiophilia' I'm not too sure you'd see a huge difference between spending $150 on a pair of headphones and $300, so you're probably better with some decent headphones around the $200 mark.
On amazon the DT770s are around $170 so those with the essence is a great combination and is well under budget.
If you want to look around a little more there are plenty of reviews online comparing them to other similarly priced models and other brands.
It probably depends more on what kind of music you listen to as to which you'd want to buy...
For example there's DT770s in 80ohm, 250ohm and 600ohm, then DT880s and DT990s all for roughly the same price. The 600ohm version is too high for the soundcard to properly handle so ignore that - but there are a fair few comparisons online comparing them all, so pick whichever you like in terms of what people say in reviews about how they sound.
I know I've only listed Beyerdynamics here, but they're the only ones I've actually looked into, and they're all made of metal rather than a cheap plastic, so the build quality is superb and they shouldn't break anytime soon.
They're also incredibly comfortable.
After that - just get any lapel, desk stand, or monitor mounted microphone for gaming. It really doesn't make any difference at all with the mic, so just the cheapest you can find. Mine was like £3 and works perfectly fine and is completely out of the way. You only need better if you're recording gameplay commentaries or recording music or something similar...
...But if you were wanting a gaming headset I doubt you'll have recording music in mind
