lewis02 :
justin.m.beauvais :
It all depends on the kinds of sound you expect and the headset you are using. If you are using a very high quality headset or expecting very low noise, then the onboard sound is probably not for you. If you just want to play games and listen to some music here and there, then the onboard audio will do just fine.
A sound card is great for gaming and better for music. Most sound cards will have better support for special audio formats that make games more immersive. They will also free up a few CPU cycles as the onboard sound sometimes pulls CPU resources.
An external sound card is awesome for audiophiles because it has the least chance of noise or interference due to the stuff happening inside the case. Sure, some are meant just for laptops that have crappy sound, but many are aimed at the extreme audiophile who wants the best DAC chips and the clearest audio. They are also pretty expensive.
So, it all depends on what you want out of your audio.
If I'm using onboard audio, would it be better to buy a headset that is connected via USB, or would the integrated audio provide better sound quality?
Your onboard sound is going to be a lot better than the cheap little chips they put in USB headsets. Also your HyperX headset isn't high enough quality to really warrant anything more than onboard sound. I hate to say it, but most gaming headsets simply aren't great for audio quality. They are good, but there are a LOT better headphones out there, and most of the time they are spending money on noise cancellation for the mic so people don't hear you munching on cheetos.
Your onboard sound should be fine as long as you aren't getting excessive noise or audio distortion. If you want to know how much noise you are getting just turn the volume up when nothing else is happening. If you hear anything then that is noise caused by something in the PC. If you can live with it, which in most cases people aren't bothered by it, then there is no reason to look any further.