Right, So if we start with the actual headset category, for around $100 you should be able to get either a Sennheiser GSP300 or a Cooler Master MH751.
Sennheiser sounds a little bit better and has a tiny bit better mic, while the cooler master is generally slightly more comfy. Both are fairly neutral with a mild bass bumb (as expected of gaming headsets) and there's very little hassle to be had here. They have enough trebble and good enough imaging not to hinder you in games. Soundstage could be a bit better though.
Step up from that a bit, we've got Beyerdynamic MMX 300 2nd gen. These are essentially a 32ohm DT770 with a rather good mic. Slightly elevated bass (including sub-bass), neutral mids, sharp-ish trebble (that's true for most beyers). Pretty good imaging, rather good soundstage for a closed-back, very comfortable. A bit too much bass for what I'd like to have for competitive games, but it adds to the fun factor.
Worth mentioning is Audeze Mobius, which while at $400 is a bit outside your budget, HyperX maked licensed, slightly less equiped clones (Orbit and Orbit S) at around $250. By no means perfect headset, it actually has quite a few issues (high clamp, pads are meh...) it is nevertheless probably the best sounding closedback headset, and a remarkably well tuned closed-back headphone, even in non-headset context. Planar drivers, 'nuff said.
Also, if you're willing to get things shippd from the US, the Sennheiser PC38x made by drop.com is a particularly good sounding headset. It's an open-back, which means recess bass, cleaner mids and high and wider soundstage are ll on the menu. Not that great if you want to bop your head to some subs and wubs, or if you want to use them in public transport, but if you've got a nice, quiet environment, consider and open-back.
That's about is for headsets, if you're willing to go for a separate headphone-microphone combo, we've got loads more options.