Dear young folks, rediscovering the power of personal MP3 players like iPod Classic. Know that retro gives you more. My personal favourite headphones for an iPod or similar device: AKG K92 (closed back) and, of course, the Koss Porta Pro (open back). Both still being made, both in the €50 sweet spot of really good sound at an affordable price. And as both are passive headphones, they last forever. No battery problems, no codec shit. Just sound. Good sound :) You're welcome.
The Koss Porta Pro is known to have cheap cables, so they might break or be ripped off (I never had that problem). So they also serve as a good way to learn basic soldering ;) Replacing the cable to get many more years of Sound is rewarding. Trust me on that.
And, trivia section, the Koss Porta Pro was introduced in 1984, the AKG K92 was introduced around 1989, as far as I can see. They both have earned their reputation for good reasons. Sure, the audiophiles will disagree, but in my opinion and experience, both are superior and reliable sets of cans for cable-based music consumption. You can't go wrong with either.

@jwildeboer Just remember the difference between open back and closed back ear cups. Open back are known to sound better, however, you will also hear all the ambient sound around you. And, as mentioned in another comment, other people will hear your music.

Don't forget about Grado's too. SR80 is a good value for the cost.