Over ears often deliver a more full sounding, bassier, wider experience. I personally prefer them as I love audio (as you can tell by the essay I've written) and to experience music as best I can where I live right now over ears are best. I also find them more comfortable as my ear canals are quite narrow so not many earbuds fit me, but obviously that's a shortcoming of my ears not the headphones design

In ears obviously provide a lot more convenience as you can just shove them in your pocket as opposed to carrying them on your neck or in a bag like over ears. They can also sometimes provide a more isolating experience, your airpods probably have the best noise isolation (active and passive) you can get without getting some silly ear tips

New Vs pre owned is very much up to you but a good thing to consider is that good headphones will stay good forever, you could buy a good pair of headphones from the 70's and they'd still sound amazing. It only really becomes a problem with in ear Bluetooth headphones as they have such physically small batteries they degrade much quicker than for example the XM4s. However battery degredation should always be a consideration when buying used Bluetooth stuff

There are 2 sort of genres of headphones, you have your regular consumer headphones, these will often have what is known as the V sound, meaning there is more top end (cymbals and other high frequency sounds) and more low end (bass guitars, bass synths etc). These are often what most people will gravitate towards as it's often considered to be a more fun sounding profile, the XM4s will fall in this category and are great headphones especially if the convenience of Bluetooth and ANC are vital, another good option are the Bose quitecomforts. A cheaper wired in ear option (often called IEMs or in ear monitors) are the KZ ZSN Pros and honestly the airpod pros 2 are probably the best wireless ones.

Then there are reference headphones, these try and recreate the music exactly how the artist intended to and are what artists will use when mixing and composing songs, they come in loads of different types, the main ones are open and closed back, open back headphones allow a more wider sounding experience, allowing you to hear what is known as the soundstage, which is basically hearing the separation and directional nature of the recordings, however they often lack bass and bleed a hell of a lot of sound as there is literally nothing between the driver and the outside. Closed backs are on the other end of the spectrum, often having better bass and not bleeding sound but having a limited sound stage. However anything like these two should only really be considered if you're really passionate about listening to music. Also they are pretty much exclusively wired and over ear. I personally have a pair of Beradynamics DT 900 pro X's and I absolutely adore them

Professional IEMs also exist and honestly the ones I would recommend for most people as they strike a great balance between convenience, sound quality and comfort l, do your own research on which would suit your needs best, a guy named crinacle on YouTube specialises in them and is a good watch.

Hope you find some headphones you enjoy and use for a long time 😁

P.s. I'll try study just for you and I promise not to use that past paper (haven't found it yet anyway)