I should imagine the most important, in fact I would say critical, thing to take into account whatever headphones and whatever headphone amp you wind up with is that, depending on which headphones you decide on, the amp is up to the task of driving the headphones properly. For example Sennheiser 600s being a relatively high impedance load as the amp sees them require around 3/4 of Watt to drive them with authority and 1 Watt would even be better. The point being that if you skimp on the wattage for Sennheisers or any other headphones with similar requirements wattage wise you will achieve the headphones' full potential. This is why I like hybrid tube headphone amos, since they tend to have a relatively high output compared to pure tube designs at the same price point. Of course with companies like Woo Audio, you can select what you need from a wide range of offerings, mostly or all of them pure tube designs. Highly recommended.

Geoff Kait
Machina Dynamica

Unless you are well-used to headphones - Grado being a good example, think carefully about comfort - it's as important as the sound. The larger fully-around-ear** headphones like the Sennheiser HD600, AKG K712, Beyerdynamic T90 etc. are the safest bets, while Grados rate low on comfort for the average user.

**Beware the term "over ear", which doesn't assure a fit without pinching the ears.

Massdrop has a Grace DAC/amp for $500. That would be my first choice.