Hy!
I've used a Beyer in studio for a while, and they're good, But I find them a little too overpriced for the quality, which is good but not THAT good.
I'd would really suggest you to try the AKGs K240, I find them of great audio quality (I have 3 in the studio for general monitoring and balancing). I also use them for games and I love the 'definition'. And you won't need an amp for them.
As far as headphone amps goes, I'd like to give a little advice. Firstly, since you're interested for listening to music and gameplay, consider the mobo of your pc. If you've had no problem thus far as in EMI clicks and so on, you're likely to not need a proper headphone amp.
But, if you're really interested, any amp worth its salt will be able to push a 250omh impedence, no sweat. You could easily get a away with a Behringer MA400 with the line out signal form your mobo.
If you want an outside converter like a DAC, because you do not want your mobo audio path in the equation, it's a perfectly fine choice, but it will be more expensive. In that case, consider a DAC with an optical input and not a usb.
Ah, you could also get a usb audio interface instead of DAC (like a 2i2 by focusrite) to be your main audio source. Connects via usb, will drive any headphone and it will actually allow you to use higher sample rates and bitdepth if you want to listen to high density audio or a game is sampled at 48Khz. It's a proper option, real pro audio gear, not gimmiky semi-enthusiast crap, pardon my french.
Anyway, the short of it is: look at AKG, it fits your demands and they are REAL pro quality. About bass boosts, do not buy a tuned headphone, if you'll grow tired of it you're stuck. Do it with a EQ in software and be happy with that, it shouldn't add any latency. For Amps, your mobo is most likely fine if it's not a very cheap one, if not, get a monochannel headphone amp (any will do) without a converter. Or go big and get a real sound interface (not the gaming soundcards and such, those add EMI and area basically marketing snakeoil), the basic ones like 2i2, presonus or m-audio will work great and will give you the option to actually one day hook up a real audio monitor, like a KRK or a Focal to REALLY listen :)!
Hope this helps!
Enjoy!