hey just unwrapped my SW3 today and joined XDA.
Im currently going through the motions of getting music onto my SW3 for this purpose.
My findings so far are this. there two options.
1. Download and install the Sony walkman APK availabe on Xda...dont have link handy. This was super flakey all day for me today on my HTC one M8 converted to GPE running 5.1. but it now seems to be working and i am currently syncing my first album to SW3. this is taking its sweet time to be honest.
2. Using google play music. Now this isnt as easy as one would hope or imagine. It relies on all your music (personal stuff downloaded from where ever and stored on phone) to be uploaded to Google Play (room for 50000 songs) from a computer.
So today i have been doing this (getting payed at work mind you), copying all music to the computer from phone, then uploading to the google play servers.
Then once all music is uploaded you need to then create a playlist on the google play chrome app with the music you want on your wear. then go into the google play music app on phone, go to settings and hit refresh. this should then show the playlist you created with cloud stored music. Once your in that playlist on your phone, you should see an option to download it. Do so.
Then go to settings again on the phone and enable download to android wear option.
this should technically auto download only this playlist to your SW3...but im yet to test it cause it literally takes forever to upload the music from computer to google play. SW3 needs to be atleast 70% battery first.
Obviously, the walkman route is the much simpler option here. But only readily available to those with a Sony Xperia phone which runs the Walkman app natively.
Hopefully there is some kind of update coming with easier Wear music management.