I use VLC. I don't use paid services like Spotify, YouTube, Amazon etc. I buy the cd that i want, then rip it and put the mp3's on my phone so i can listen to it in my car (new cars don't even have a cd player anymore haha). Pro about this app is that it plays almost every file, had a easy to browse library and very used friendly. The standard Google app (Google Music i think) is a pain in the *** to navigate around, so i started to look for something else. Too bad there isn't a Winamp mobile version.
I use Google Play and YouTube music, I pay for Google and automatically get YouTube music as a result.
They work for me but I agree with ICe that the navigation could be better, ironically in an iPad it looks better and works better than on my Android phone
When I first used Google Play Music I ripped my CDs on a laptop and dragged them into Google Play Music which allowed me to play them via data or download them. I'm not sure if that's still an option but if it is and it's still free, albeit with a cap on how much data you could save, maybe worth a look.
I've also ripped my CDs over the years and just the other week updated my library and ripped everything onto an SD card and usb stick for car use as I find it easier than fiddling with a phone.
I used to use Spotify but switched over to Apple Music. Spotify's library implementation is horrible. Apple Music allows me to integrate my vast ripped library with stuff I now only "own" on the service.