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.