If I were doing a site such as you describe, I would probably make a Custom Post Type for “Artists”, another Custom Post Type for “Albums”, and would link them with the “Posts 2 Posts” plugin.
It’s easy to use and well documented.
That way, you can later easily attach images and galleries, mp3s, and whatnot. Using taxonomies has many limitations.
And you could add a “genre” or “styles” taxonomy, to tag your artists and albums with.
Just my 2 cents 🙂