I started my experience with upgrading my iPad Air and then starting using the service. Apple Music obviously had my iTunes purchases, playlists, and had subscribed the artists whose music I own in the Connect automatically for me. Discovering new music is quite easy. "For You" -tab provided good recommendations and playlists for me. Curated playlists seem like a good idea and I found quite many songs from them.
I was surprised by the many crashes when browsing through artists and albums on my iPad. AirPlay playback via AppleTV to my amplifier was also very unreliable from iPad. Quite often the songs just went silent after few seconds of play, and only when I skipped to next song playback resumed. AirPlay from my iMac worked without any problems so could be an issue in my WiFi setup somehow.
I've never been a big radio fan, and rarely listen to Internet radio so Apple's Beats 1 is not for me. I also don't see a lot of added value in the "Connect" social media. Hardcore music fans will anyway follow their favourite artists in other social medias, and artists simply have to put their stuff to FB, Twitter, Instagram, etc. anyway since majority of world will not be using "Connect". Apple Music team could just focus their efforts on making integration of Apple Music to existing SoMe services and Web (provide API!) as fluent as possible instead of trying again to reinvent SoMe.
Personally, I have never spent a lot of money to music. I've been buying 3-4 albums of music from iTunes every year for about 10 years now and additionally I've got plenty of mp3 files from my student years. I've also been using free Spotify to listen to current hit singles. Streaming service like Apple Music or Spotify Premium would be a better user experience for me, but I'm not yet convinced that benefits are big enough for me to justify additional cost. I'm probably going to enjoy my three month free trial and after it is over go back to using combination of free Spotify and sometimes buying songs from iTunes.
Edit: After upgrading my Mac to 10.10.4 AirPlay from iPad to AppleTV has worked without any issues. Perhaps discoveryd was messing up something in my network.