Determine how close musicians will be to open microphones. Professional studios typically use closed ear headphones with large, soft ear cups to completely enclose the ear and seal the unit against the user's head so that no sound escapes into the room to bleed into a microphone. Evaluate headphone leakage by feeding a reasonably loud signal. Remove them and press the ear cups together. Little to no sound should be heard.
Consider how loud the headphones are. Musicians will typically prefer loud mixes, so headphones of low impedance, under 100 ohms, may be preferable.
Consider the musicians' comfort as well. Closed ear headphones are the heaviest and least comfortable, so try several models for wearability. If headphones are used only for tracking performances on long sessions, sound quality can be dropped below comfort as a priority. Single-cup headphones are available and handy for recording singers who want one ear uncovered.
Calculate how much mix monitoring will be done through headphones. Open ear headphones generally provide more balanced sound and provide the user with greater comfort, but at the cost of isolating the sound from the outside world. These may not be suitable if there is much ambient room sound to block.
Choose a price range based on typical use. Some home studios require much mixing done through headphones. The cost/quality factor applies here. Headphones used to occasionally check elements of a mix can be less expensive than those that are frequently pressed into mixing duty in place of monitor speakers.
Consider how you work and how headphone design will affect your work flow. Cable style varies with wires going to either one or both ear cups. The cable may be straight or coiled. Each consideration may become important when spending hours working a hot mix.