It depends. For tracking, a good pair of over-ear headphones is best. For location recording, the same pair is great, but I’ll often wear in-ear monitors instead because they fit in a pocket and the headphones take quite a bit of bag space. For casual listening, anything works - even the Bluetooth ones that came with my phone - though there’s obviously a quality difference. Really, though, as long as you can hear what’s going on and are familiar with the changes the headphones (or whatever) make to the incoming audio, you’ll probably be okay… aside from comfort and portability, which is why I keep IEMs as well as cans.
Not sure if they have any still, as inventory changes constantly, but at one time I bought a couple of dozen for the computer lab I put together for the small private.school where my wife was teaching, and later bought some to use in the ER for listening to dictated radiology reports. As usual, YMMV.
Here’s a link to some they might have.
Over ear > in ear* > on ear > earplug-like buds. Earplugs cause a massive amount of discomfort for any reasonable amount of time (more than 30 minutes), so have to use (over ear) muffs when hearing protection is required. Thus the preference for headphones, as well. On ear (headsets) can work, but not for extended periods of time (hours). The only disadvantages for over ear is they tend to block out other sounds and, if wearing something on the head, any thickened portion can cause pressure with the band. * I consider “in ear” as the gentle style of buds that do not go in like earplugs.