The impedance of headphones is of concern because of the output limitations of amplifiers. A modern pair of headphones is driven by an amplifier, with lower impedance headphones presenting a larger load. Amplifiers are not ideal; they also have some output impedance that limits the amount of power they can provide. To ensure an even frequency response, adequate damping factor, and undistorted sound, an amplifier should have an output impedance less than 1/8 that of the headphones it is driving (and ideally, as low as possible). If output impedance is large compared to the impedance of the headphones, significantly higher distortion is present.[11] Therefore, lower impedance headphones tend to be louder and more efficient, but also demand a more capable amplifier. Higher impedance headphones are more tolerant of amplifier limitations, but produce less volume for a given output level.

The DT770 is fine – not basshead, the COP is the same size and configuration as the 770, and both of those, large though they are, are “tighter” built so they feel less clunky than the M50. But the biggest problem for you is that the smaller headphones under $200 almost all have a steeply rolled-off treble, which is trouble for the more refined type of music. One possible exception is the Harman Soho.
In the professional audio sector, headphones are used in live situations by disc jockeys with a DJ mixer, and sound engineers for monitoring signal sources. In radio studios, DJs use a pair of headphones when talking to the microphone while the speakers are turned off to eliminate acoustic feedback while monitoring their own voice. In studio recordings, musicians and singers use headphones to play or sing along to a backing track or band. In military applications, audio signals of many varieties are monitored using headphones.
Over-ear and on-ear headphones effectively block out outside sounds, allowing you to hear your music or whatever else you're listening to crisply and without distraction. Over-ear headphones are sometimes known as full-size headphones because they completely envelop the wearer's ear. This results in what's known as passive noise reduction, which makes these some of the most-preferred headphones available. The only drawback is that your ears and the skin around your ears can get warm and sweaty. These are usually the heaviest type of headphones.