I use the Pandora app on my iPhone and listen to it when I'm getting ready (makeup, etc.). I first went to Pandora.com on my computer and set up a few playlists. But if there is a genre name, they probably already have playlists. I just started listening to one called Alternative Endurance mix for working out. This introduces you to new music, and sometimes it's music you have already heard but didn't know the name of it. This way you can take notes and search for that song somewhere, like the public library. Also I have playlists for my favorite artists, and there is music from them, plus other music that Pandora thinks you might like, to add to your collection of what to look for.
My public library offers three free downloads a week from a site called Freegal. The songs on Freegal are all Sony artists, and Sony has hundreds (?) of smaller labels under their umbrella. So if your public library has a website, see if they have the Freegal service. You need to log onto Freegal w/ your library card number, and then you're in. I downloaded a few Adelle songs off of there, Michael Jackson, Pumped up for Kicks, some other stuff that I was just looking around and found them there. It's pretty fun! Good luck!