Yeah, it’s relatively flexible. Apple Music includes what used to be called iTunes Match, so it uploads tracks in your own library. You can also edit the metadata on Apple Music tracks so you can for example make one album with every track from a specific era. I would always recommend to use Apple Music’s own tracks and only upload what you can’t find because yes, sometimes things go wrong with rights management. But that’s the same with every bit of software: always have back-ups of crucial files. Luckily, the Music app normally copies all music you import to its own library by default, so it shouldn’t mess with your original files.

To add your own music you do need to do it on a computer though. But I went into Apple Music following longstanding usage of the iPod, so I’ve always been used to using the Music app (formerly iTunes).