Getting the right headphones?

The buzzing sound is an impedance mismatch. Skipping all the boring electronics stuff, you want a headphone/earphone with a higher impedance and lower sensitivity. As a general rule, full-size headphones have higher impedance than portable headphones, which in turn have higher impedance than earbuds/in-ear earphones. I can recommend the Koss KSC75 or Koss PortaPro, which have 60 ohm impedance but there are many others. For earphones the HiFiMan RE0, Brainwavz M1, and Phonak earphones are known to have high impedance but I'm sure there are others with 32 ohms or more.