Oh headphones. I use Beyer Dynamic DT 770. For small equipment look for something below 32 ohms, and for equipment with more power I use 250 ohms.

Edit: sorry,got interrupted again. If you use headphones rated at 250 Ohms and plug them into a portable device, it's like pulling a Garbage Truck with a Moped, so the resistance rating is probably the first thing you should look at. If you want the ultimate in sound quality, typically ratings of 250 Ohms or thereabouts are better, but if used with smaller devices often require a separate Headphone amp.

Other differences in headphones is open shell or closed shell designs. Open shell provides a better sound stage, but I use closed shell headphones because I need to exclude my environment. Someone else has a radio or TV going all day and I can't get away from that space.

Did I miss something? Probably...