Apple
According to Apple blog 9to5Mac, Apple is disallowing Apple Music from its cheaper iPods to prevent piracy. This way, Apple ensures no customers can save their songs onto an Apple device after their subscription is canceled. Apple needs WiFi to authenticate an Apple Music subscription, and the cheaper iPods aren't built with WiFi capabilities.
However, Apple Music will work on the new iPod Touch, which starts at $199 for 16GB of storage. That device, which has major improvements over the last iPod Touch according to this thorough Ars Technica report, includes the iOS Music app and WiFi support, which means Apple Music will work on that device. But if you try syncing Apple Music to an iPod nano or shuffle, you'll see a notification that says, "Apple Music songs cannot be copied to an iPod."
It seems bizarre to say an iPod won't work with Apple's music service, but for now Apple Music is limited to WiFi-enabled iOS devices only. That said, you can still store music on your iPod nano or iPod shuffle: anything you purchase in iTunes, or any DRM-free music you own, will still work on those devices.
Hopefully, Apple figures out a way to get its entire iPod family working with Apple Music. 9to5Mac's Mark Gurman suggests Apple change its software to "accommodate authentication of Apple Music subscriptions through iTunes once a month, at least for users that want to take that step to get their offline tracks into their new iPod nano or shuffle."
Apple Music is currently available for iPhones and iPads running iOS 8.4, Macs running OS X 10.10.4, and the new iPod Touch. New users get a free three months of the service, but once that expires, you'll have to pay $9.99 a month for a single membership or $14.99 a month for a family of up to six people.