I'd also very strongly recommend F-Droid. TBH I can't really speak to the quality of music apps on it - I just use VLC - but it doesn't require an account and it has lots of good apps.
I use Auxio from F-Droid. It's quite simple (which to me is a benefit) and my only real complaint is how similar shuffle on and off look on Android Auto. It handles non ASCII titles correctly where some others didn't (from what I remember due to weirdness with the Android media store) and it picks up new media/edited quickly and reliably which can be a sore spot with others. I don't know how Android's media store is apparently so incompetent that most music apps don't work correctly using it.
can also vouch for Auxio - happy user of 5 years
No album shuffle (like on iPods, like taking random CDs from your shelf; https://github.com/OxygenCobalt/Auxio/issues/221) and no way to correct headphone's frequency response (either AutoEQ presets like PowerAmp or at least a good enough parametric equalizer) makes it a no-go for me.
I use the F-Droid apps Transistor to listen to streaming radio and Antennapod for podcasts on an old phone: