I'll report more fully on Apple Music in the future, but here are some preliminary thoughts on how it interacts with Family Sharing.
Up until now, my family has generally shared a single iTunes Apple ID, and has used Apple Match. We have a "server" in the house with around 8,000 songs on it, mostly ripped from our collection of CDs (we had a lot of CDs, because we are old).
Apple Match allowed each of us full access to any song on that server. I did not realize this, but apparently Apple Match would not work if different family members were using different Apple IDs, all linked under Family Sharing; only songs bought on iTunes would be available on each device in that case.
Since a big part of Apple Music is music discovery - the service suggesting playlists based on individual music preferences - it seemed a good idea to finally switch my family to using Family Sharing for iTunes. My classic rock/classic rock/rock/rock/alternative/alternative doesn't mix well with my kid's pop/pop/hits/hits and my wife's classic rock/classic rock/rock/rock/alternative/country/pop/hits/
We had already been using Family Sharing for iCloud; iOS allows you to use a different ID for iTunes/music than you use for everything else iCloud-related, and we had taken advantage of that.
So I thought this would be simple; just go to Settings | iTunes & App Store and click on "Apple ID: ..." and enter the same Apple ID we had been using for other iCloud functions.
This worked fine on my kid's iPhone, but on my wife's iPad all hell broke loose. Apple Music kept insisting that we start a new free trial for her; it failed to understand that she was under the Family Sharing plan I had already set up on my own device.
After much experimentation, the following procedure solved this problem:
1) Go to Settings | iTunes & App Store and sign out
2) Go to Settings | Music and uncheck Apple Music
3) Kill the settings app and Music app (by double-tapping the home button and swiping both apps upward)
4) Go to Settings | iTunes & App Store and log in the family-member Apple ID
5) Go to Settings | Music and check Apple Music.
6) Launch Music
Though this solved that problem, we next realized that none of the music in our personal collection was available on either my wife's or kid's devices. This despite "iCloud Music Library" being turned on for each device.
After some more research, I discovered that iTunes Match does not share personal music (i.e. music not purchased on the iTunes store) among Family Sharing members; presumably the same is true for iCloud Music Library.
This is a bit of a pain since not all of our music is available on Apple Music (e.g. The Beatles).
If we figure out a solution, we'll let you know.