I wouldn't really go for these 'Gaming' labelled headphones as they are not exactly designed for music. The EQ on them is tuned to emphasize the bass, and often quite largely. While it may sound (haha, pun :3) like a good affair for gaming, and listening, you may find that you'd want to listen to something with a little more focus on mids and trebles, such as classical. You don't want overpowering bass for that, because it'll likely drown out those higher frequency ranges. :) Plus, overpowering bass can sound pretty muddy (I'm looking at you 'Beats Headphones').
For a general all-round good pair, I can recommended brands like Sennheiser, AKG, Beyerdynamic and Audio Technica. If you have a low budget for this, I highly recommended Sennheisers, like the HD 419/429 (the former being the more bass-focused pair and the latter being more evened out, none too overpowering or unbalanced) or perhaps going minimum and buying a pair of HD 201/202's. Preference plays a big part in what pair you go for though. If you want everything to be smooth and evened out (a flat sound signature), you might want some Audio Technica's, possibly the ATH-M50X's. :) They are all good quality, but everyone has a preference. See if you can try out a pair before buying. It makes the biggest difference knowing what you're getting into.
Hope I've helped, and hopefully I've not broke any rules making this first post. (Sorry admins. It would take too long to read all the rules, but I skim-read it and I get the general idea, I think :3 derp)