Headsets generally don't perform as well as a separate microphone/headphone combo, so if you can, I'd recommend buying separately rather than looking for a headset.
I use the blue yeti which is around $100, but I bought it on sale for about $75. The quality (as I've been told) is great. It has a headphone jack too so you can monitor your mic as well as act as a playback device to send all your audio through. As always, a lot of microphones that are more expensive will probably sound better if you're willing to expand your budget, but if all you're using it for is communication/voice recording and not studio recording, then it is a perfectly fine mic to consider. If it's not in your budget and you're looking for something cheaper, the Blue Snowball, their $50 option, is a great choice also, although doesn't sound as good in my opinion (still great though). As for clip-on microphones, I'd say Antlion ModMic is probably your best bet.
As for headphones, like Hoplite said, it depends on what you're looking for. Open-back headphones will have a more natural sound but will bleed more, meaning people around you will probably be able to hear whatever you're hearing too to some degree. You can read more up on that
here. I don't really have too much experience with different headphone brands, and I'm still using an old set of Astro A40s (plugged in through my blue yeti). However, what I've read/seen is that you generally can't go wrong with Sennheiser or Audio Technica (although many have said that the ATH-M40X is way better than the ATH-M50X since the latter is too heavily focused on bass over middle/treble). I would just search through some reviews online and weigh out your options and read some reviews.
