Do you have a Mac or a PC? How you copy your music depends on how you have your library managed on the computer. You could plug the phone into the computer and copy the files over the USB connection.
Alternatively, you can upload everything (I know what you said, stick with me) to Google Play Music using the Play Music manager
https://support.google.com/googlepla.../1075570?hl=en then you can select (when on WiFi) what songs/albums you want cached locally, choose the "download" option. When you want to listen, be sure the "downloaded only" option is selected from the slide-in menu on the left. This way you don't have to have space for EVERYTHING on your phone.