How can I backup everything on my phone before a factory data reset?

I'm ready to throw my Moto G at a wall. Or off a bridge. Its got such a lag that its almost useless. There's at least a 3 second delay when I do anything from touching a letter while texting, to loading my browser (that doesn't load half the time anyway), to using the dial pad. I've removed everything except the Verizon-mandatory apps and my music, which as my Moto G only has 5 GB of storage, its less than 100 songs. I ran multiple scans using AVG and found no threats. I've cleared cache already, and no such luck. The internet is also causing problems. It almost never loads, I get the "Oh snap!" message at least half a dozen times a day, and the lag is ungodly. I'm going to try a factory reset as a last resort, but I can't seem to get my music off the phone, so does anyone know of any way to do a backup so I don't just lose all my music? It took me forever to download it all and I will be CRUSHED if I have to try and find it all again.

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