+1 on Google Play Music.
It's easy to get started. Download the
Music Manager application and point it to where your iTunes music is stored. Google will then upload all of your music into Google Play Music ("the cloud"). Depending on your upload speeds, this could take a few hours - it's best to set this to happen overnight. Once your music is uploaded, you'll have access to all of your tracks via the Google Play Music on the web as well as the
Google Play Music app for Android.
If you're on a data plan that's limited, you may not want to stream Google Play Music all of the time. If you know what songs you want to cache, you can "pin" them in the Android app. It's best to do this while you're on your home WiFi. I like to set up play lists and if I need to cache them for offline playback, I can "pin" the entire list to my device.