Deutsch Als Fremdsprache

Die Ärzte and Farin Urlaub could work too. (probably, I’m not learning German)

I would just add that pretty much any kind of music can work. The most important thing is you like it. Sometimes you have to try different bands to find something where the vocals are clear and the lyrics are interesting. As long as you can find the lyrics online, you should be good.

My thing is mostly metal. There are a lot of good bands, way more than just Rammstein. Eisbrecher, Erdling, or Saltatio Mortis, for example.

Or all different kinds of rock. You might like Sportfreunde Stiller (indie/alternative rock) or Revolverheld (alternative rock/pop). They both sing pretty clearly, not very fast, and use everyday language.

Oh, and Lyrics Translate is pretty good for translations.