Well I need headphones for music and games as well. Should be comfortable. Over-Ear. Isolation isn't an issue for me.
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Well I personally prefer Closed Headphones to provide sound isolation from nosiy environments and some privacy.
Anyways based on your budget you look at incase if Closed Headphones:
1) Audio Techica ATH M50x for about 150$ or M40x (if you want really neutral Flat sound across the board) for about 100$ max.
2) Sony MDR 1A (which Btw I'm currently using) as they are super comfortable for long listening session and the Bass is just awesome and not overbearing or Overemphazing like those Beats headphones and overall very Good build quality as you migh expect from Sony. But bear in mind it might cost over 150$ to nearly 200$. It's expensive but trust me its worth it.
3) Audio Technica ATH MSR7 (priced slightly over 150$)
4) VModa Crossfade M100
5) Sennheiser Momentum
6) Beyern Dynamic DT770 Pro-32
7) Kingston Hyper X Cloud (it basically a gaming headsets with 7.1 Usb card but it also provides good listening experience).
8) Sony MDR-7506 (It old but GOLD) and cheap too, have a look at it.
And for Open back Headphones:
1) Sennheiser HD 598 Special Edition (Neutral sounding with more flat frequency response) I have used it in past, but I sold it as I need closed back Headphones.
2) Beyer Dynamic DT990 Pro
3) Hifiman Edition S (it can become open back and closed with plates) and THIS Is personal recommendation.
Overall all these aforementioned headphones don't necessarily require an Amp to crack volume or power them. They are all pretty efficient and will sound great whether you power them Pc, laptop, IPod etc
For most Peopel Audio Technica ATH M50x does job and it has been proven winner amongst the experts as well.
Sony's MDR 7506 is also bang for buck, you can't go wrong with it. Closed design and highly rated by experts, But sadly it has 9.8 foot not detachable cable. But keep in mind its price nearly 100$ so you can't ask for more in this price range.
Kingston Hyper X Cloud 2 is also a good choice although it's primarily a gaming headsets but it does a good job on music too.
I hope my answer suffices you bro.
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