I am not very familiar with Google music, but I know some DJ Software (mostly on tablets) supports the use of things like SoundCloud and Spotify. Remember though that using Spotify outside of your practice room for the purpose of DJ-ing is illegal!
Our advice is to always buy the tracks you want from a reputable source in high sound quality (lossless).
If you have never DJ-ed seriously before, I’d say the XDJ-RX is a bit too advanced for a starter. As far as I know you can’t use Google Music with RekordBox or RekordBox DJ.
Read some of the recent topics on how to pick the right software and controller on the forums here (use the search or go down the list) to get a better idea about how to make the best decision for you!