I use a pair of Grado SR80i headphones for general use; they have some of the best sound I've ever heard in headphones (compared to a Best Buy rack of phones; sounds better than even $200 Sennheisers and $400 Beats and Bose). They have a lot of downsides though. The open back design lets a lot of outside noise in which can be annoying in a busy house or with a loud PC. Also, leaked sound may disturb others if you like your music loud. The headband is also way too tight and will feel like a vise grip for the first few months of use.
I don't have any specific suggestions other than to stay away from "Gaming" branded 'phones if you're planning on doing anything other than gaming. The choice depends on what you'll do with them the most. If you're going to be using them in noisy places, you'll probably want closed back headphones and possibly noise cancellation. If it's only going to be at your desktop, open back will sound the best. For gaming, sound quality is less important than stuff like comfort (for long hours) and surround sound (for FPS footstep tracking, mostly).