[Reasv]

So, I'm new in this subject and the only headphones I've ever owned were 25$ sonys and I now use the logitech g930 headset.
Knowing that I would get much better audio quality for a lower price, I started doing some research on headphones and I think a good set for me would be either the Sony MDRV6, MDR 7506, AT M50 or AKG 240 also based on some recommendations I got. I don't care about strong basses since I mostly listen to classical/instrumental/orchestral music. Or maybe something else in the same price range would be better, I don't know. I never listened to any of them so I can't actually know which is better.
 
One last thing: I want circumaural headphones.
About open/closed, I'm not sure. I heard open sounds better. But closed has the advantage of insulation. Not that I need it that much, but not leaking audio seems like a plus. I'm going to use them in a relatively quiet environment so the only thing I could want from closed 'phones is that others won't hear what I listen to, it's not too important though.

 

[PurpleAngel]

Takstar Pro 80 (Gemini HSR-1000) closed headphones.
To me they are the best sounding headphones for under $100.
If Sony put their name on them I'm sure they would sell for $150.

 

[Dragonzeanse]

The Sony MDR-V6 and 7506 are the same headphone. ATH-M50s are a bassy, v-shaped headphone. AKG K240s, I have no experience with. I don't think you'll regret having the MDR-V6/7506, though. A surprisingly good headphone and they sound very neutral. They aren't open, of course, so they won't have the soundstaging K240s do.

 

[Captain Magenta]

  So, I'm new in this subject and the only headphones I've ever owned were 25$ sonys and I now use the logitech g930 headset.
Knowing that I would get much better audio quality for a lower price, I started doing some research on headphones and I think a good set for me would be either the Sony MDRV6, MDR 7506, AT M50 or AKG 240 also based on some recommendations I got. I don't care about strong basses since I mostly listen to classical/instrumental/orchestral music. Or maybe something else in the same price range would be better, I don't know. I never listened to any of them so I can't actually know which is better.
 
One last thing: I want circumaural headphones.
About open/closed, I'm not sure. I heard open sounds better. But closed has the advantage of insulation. Not that I need it that much, but not leaking audio seems like a plus. I'm going to use them in a relatively quiet environment so the only thing I could want from closed 'phones is that others won't hear what I listen to, it's not too important though.

I've owned the V6 and the K240.  I found the V6 to be quite detailed but a bit 'tinny' sounding and ultimately not outstanding in any way.  The K240 have a really nice warmish sound with nice midrange and are good with most music. I would say they are a clear step up from the V6 but really need to to be amped to sound like they should despite being only 55 ohm. 
 
I would also seriously consider the K550/551 due to the great discounts at the moment as they are in another league altogether and are not so amp dependent though I would budget for a cheap dac/amp such as a Fiio as it always improves things to a degree.  One thing I find to be an issue with the K550 is they can sound a bit harsh with bright or poor quality recordings but this can be remedied with a warm sounding amp. Despite this they are incredibly detailed and refined and easily worth double what they are selling for (at least here in the uk anyway). They also don't sound closed and leak very little sound as long as you have a good seal. 
 
One thing to also note about the K240 - the studio version is cheaper but without the bells and whistles of the mk2 though they are the same headphone.

 

[Notus]

My vote goes for the Akg K240s or the K240 mkII depends on the price. I think they would work nicely with the genres you mentioned.
They do need some sort of amplifier to power them.