The number one rule to understand when embarking on your headphone-search journey is to understand that there is no one headphone to rule them all. Like automobiles, headphones are made for different purposes. You have the supercars, roadsters, SUVs, 4x4s, sedans, to the compacts, and you chose what’s best for your day to day needs. There is no one car that can tackle snow and win races on the drag strip. The sooner you understand this fact, the more money you will save.
I tend to regard the M50 as the minimum for hi-fi listening with no apologies for limitations. But if you have to go cheaper than the usual $125 USD for the M50, the B&O Form2 with a simple bass boost gives a real hi-fi sound, and it should be available for about $100. The Beyer DTX-501P (similar to soundmagic P30) is good for $100, but needs a slight treble boost. The LSTN Fillmore with wood cups is somewhat colored, but still a good listen and good for $100. Below $100 are the Sennheiser PX series – not hi-fi by any means. There are several good IEMs below $100, and Apple Earpods with a Dirac or Accudio Pro player are very hi-fi, and cheap.
A: What you plug your headphones into can significantly affect their sound, and the quality of the amplifiers built into portable CD/MP3 players is generally awful. It's not their fault: the little guys have to power their electronics and their internal amplifier using a few puny volts. Even some of the better home AV receivers' headphone jacks offer highly variable sound quality.
One thing I suggest to prospective customers for a specific headphone, if I have that headphone on hand, is for them to suggest 2 or 3 music tracks by a particular artist and composer that I can sample on that headphone, not so much for me to suggest how it sounds, but mostly to check if that headphone has any real sonic issues with that music. For example, a headphone that’s ideal for classical and acoustic music might sound too harsh with metal and industrial goth.
Although some headphones available are wired, many more are available that are wireless, and use Bluetooth to enable your music to be heard, even if the stereo or other device is several feet or even a few rooms away. Wired headphones deliver superior sound quality to wireless and Bluetooth because there's no chance of picking up interference from other devices, which sometimes happens with wireless headphones. In addition, wired headphones have no batteries to power them, so there's no chance of interruption should the batteries wear out.