What should a musician look for when buying a pair of headphones? Is there any “standard equipment” I should be aware of that practically everyone uses? Are headphones a general purpose tool, or do you use different sets for different situations?
You definitely want different sets for different situations.
For playing live, you first want something with very good isolation. Then, depending on how and why you use them, you want to think about things like how easy and fast is to put them on/off, how easy is to move around with them, and their frequency response.
You might not want them to be as accurate as possible, you might want a curve in certain wanted/unwanted frequency ranges (which can be done by eqing, but if it's a specific curve you'll constantly want, having it as the default tone of the headphones is very useful, more so if you don't have a sound engineer).
For recording (and pre and post production in general) in a professional studio you want them to be as accurate as possible. You want the best frequency response you can afford. Unless you are playing a live session or at the same time as other instruments, isolation is not important.
For home/practicing/home studio isolation might become a priority. Street, neighbors, kitchen, there can be a lot of distracting noise around you.
An industry standard for many years now is the Beyer set that you see on tv. frequently. Not sure if brand recommendation is allowed ! But - your or another person's particular needs will be factors in choice. Sound bleeding out. Isolation from external sound. Noise cancelling. Good bass/treble response.Comfort. On- ear/in-ear/over ear.Adjustable volume/balance.Max. vol. capability.All factors that make it a rather subjective choice, often obviously solved by Beyer...