iPod shuffle. There is no screen so it’s universally designed for the blind.

I haven't tried any of these, but these are the ones I know about.

Sony A series MP3 players that have quite big screens, A40 or A50. A100 also runs Android, that is probably the most configurable. And there is the iPod touch from Apple.

This may be a bit pricy but if you have an iPhone, you could get an Apple Watch. They can download music and play them to Bluetooth headsets. You could also go the way of an iPod Classic. They use spin wheels with voice over, so super easy to navigate and can store a lot of songs. If you’re looking for some hi-res audio, I personally know of the Fiio M9 but I don’t know if it has voiceover or accessibility features.

I have a Sansa Clip MP3 Player that I use for playing music and podcasts. The display is very small. If you use it to listen to random songs or long podcasts it works well without having to look at the screen. The loading process is simple drag an drop from the file manager.