Welcome to the forum!
Headphones come in 2 “sizes”:
- On-ear, the ear-cushion sits on your ears
- Over-ear, the ear-cushion sits around your ear
And three “systems”:
- Open back, the cups are designed in such a way sounds from your surroundings can easily reach your ears. These typically have a flatter frequency response.
- Semi-open, the cups somewhat limit ingress of noise from your surroundings
- Closed Back, the earcups block most of the surrounding noise. Typically closed back headphones have more bass.
AKG K-240 should work for you. Has been a long while since I had a pair on. From what I remember they do a great job with mids (the main part where music/sounds happen). Bass is on the light side, meaning there is not a lot of it. Depending on your tastes in music, this could be a deal breaker.
In case you need a microphone aswell, HyperX Cloud II come to mind. I don’t have hands on experience with them. A friend had them and only replaced them when he stepped up his audio game.