1) Be wary of “gaming headsets”. They generally focus on the marketing and aesthetic more than on the sound quality or the overall performance to price.
2) Be wary of celebrity headphones. Again, a sizable portion of the budget is focused on advertising rather than functionality. In all fairness, upon trying out a few of the Beats by Dre headphones, I do conclude that they have improved in quality quite a bit since Apple acquired them. However, you can still easily find headphones which are just as good for half the price.
3) Go for a balanced sound. Headphones which have a lot of bass (i.e. Skullcandys) initially sound very rich and heavy to someone trying them on for a few seconds, but they do not portray the sound accurately and it sounds like mid and high frequency sounds are compromised.
4) If portability is chief concern, earbuds can definitely work. However, headphones are superior in sound quality, comfort and they are less fatiguing on the ears generally.
5) If it is an option, headphones with a detachable cable are preferable. If something goes wrong with the cable, the entire headphones won’t be unusable (you can just replace the cable). Also, you are able to buy a shorter cable for portability and a longer (perhaps coiled) cable for certain home usage (such as watching television).
6) Decide whether you want an open or closed sound. Closed headphones generally are better in blocking noise, preventing noise from leaking and they offer a very densely packed together sound. However, open-air headphones add a certain atmosphere of the sound that gives it personality, a surround-sound feel and the feeling like the listener is at a concert.
7) Try out different brands of headphones. Before just going to a Bose store and concluding that they are the absolute best, try other good brands too. If you live near a Guitar Center, you may be able to try out other ones there. You can also order other brands online and return them if you don’t love them.
8) Which are the best brands of headphones? Subjective. I’m a big fan of Sennheiser, personally. Audio Technica, as well. Other respected brands: AKG, Grado, Shure, Beyerdynamic, Sony.