Do you have a memory card? If so, you need to make a folder named Media > Audio > your music goes here. You could also upload your library to Google Music and just stream everything.
I have a 16gb card on mine that I store the music on. Tha way it doesn't use up any of my internal space. I have about 780+ songs and so far have only used about 4GB of that card (that 4GB also includes lots of pics and videos so it's not all music).
Streaming from Google Music only works if you have decent data speeds. If your speeds and coverage are anything like mine you'll constantly be buffering. Easiest way to put music on the phone is to get an sd card, plug your phone into your computer, select disk drive, then drag whatever music you want over to it.