I already own a few headphones, namely the Audio-Technica ATH-Pro500MK2, ATH-T500, Sennheiser PX 100 II & PX 200 II, and the Philips Downtown and Uptown (Rule #3). I’m thinking of adding a new one and I can’t decide between the Beats Solo 2, Grado SR80e, and Sony MDR-10RC (budget constraints). I listen mostly Pop/Rock and Classical music and I have a cheap (Fiio E06) headphone amplifier.

For older models of telephones, the headset microphone impedance is different from that of the original handset, requiring a telephone amplifier for the telephone headset. A telephone amplifier provides basic pin-alignment similar to a telephone headset adaptor, but it also offers sound amplification for the microphone as well as the loudspeakers. Most models of telephone amplifiers offer volume control for loudspeaker as well as microphone, mute function and switching between headset and handset. Telephone amplifiers are powered by batteries or AC adaptors.
Earbuds have small speakers that rest on the ear canal of the wearer. These are usually much less expensive than on-ear and over-ear headphones and reproduce the sound well. However, outside sounds, such as traffic or power tools, can get past the earbuds and interfere with your enjoyment. Earbuds also don't stay in place very well if the wearer is moving much, such as exercising. These also are lower fidelity than on-ear and over-ear headphones.