The Beyerdynamic DT-990-Pro-250 is the highest fidelity headphone you can buy for under $200. I own this one, and it’s amazing. I’ve spent a lot of time examining headphone lists created by audiophiles, and this headphone was recommended many times.
It’s an open headphone — this mean others around will be able to hear your music. I recommend using a mini-amplifier with these headphones, you intend to use them with a portable MP3 player. I have a Fiio E10 USB DAC Headphone Amplifier and it works well.
The only other headphones that can compete at this price level are the Sennheiser HD 598 Headphones and the Audio-Technica ATH-M50 Professional Studio Monitor Headphones.