I occasionally use Pandora and Spotify to find new music and artists. I actually find a lot of new music from suggestions on YouTube, as someone previously mentioned.
Re: How best to organize music on my Galaxy S5
Not sure what exactly you're looking for, but I'd recommend Rocket Player. I've been using it for quite awhile now, and it's easy to sort files.
I had this exact problem with my last software update. I ended up deleting a lot of apps and photos to clear up space. Once I had 3GB of free space, the update finally installed without any problems.