Dale: There are so many types of amplifiers (and DAC’s with amplifiers) that there is no shortcut for studying all of the options, unless you settle for the most generic approach. Important things to consider are power – if you don’t have enough power for your headphone and the dynamics in the music, clipping will result. Sometimes the clipping is “soft” and not readily noticed, but eventually you would discover that much of the detail goes missing or gets veiled with limited dynamics. Another consideration is whether to use a DAC, which may be a separate DAC or built into the same enclosure as the amp. Most DACs will improve the sound over the DACs that are built into computers, but when a DAC is available to replace the DAC built into most cellphones and low to mid-priced music players, you can usually expect a much greater improvement.
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.