I have tried google play, and it is worthless because if I add a song to my PC it will upload to google play on my PC, but will not upload the added music to my phone.
If you use the Google Play Music app on your phone and don't have it set to show only downloaded music, you will see the files the music manager uploaded from your computer. If you want to cache them locally, find the music you want to download, tap the 3-dot menu on that artist, album or song and select to download. You can then listen to that music when offline.
I use MX Player - it plays most file types. (Whether an app will play a particular file depends on the type of file - the stuff to the right of the rightmost '.' in the file's name.)