The ethernet version also can connect via Wi-Fi, but for best performance you’d connect to your router, correct. It will automatically recognize that there is a wired connection if you go that route. I believe it might do a “are you connecting wired/wirelessly” prompt, but once you select wired, and assuming it’s already plugged in, it will handle the rest.
If you go with Wi-Fi it will pair the same way any Wi-Fi device does: bring up a list of nearby connections, you select the one you want and enter your password
By default, your iTunes library is tied to your Apple ID, which you created if/when you ever bought music from iTunes, or set up another apple device, etc. And that Apple ID is how you log in to Apple Music.
In theory iTunes Libraries and Apple Music are separate, however some users have reported that the cloud synced version of their iTunes library (a feature of Apple Music) got deleted if they stop subscribing to Apple Music for 30 days. My understanding is the files on your physical hard drive for whatever computer has your iTunes library now
should be unaffected by this.
To be completely certain, you could create a
brand new Apple ID that you use *just* on the Apple TV, but any movies, tv shows, music purchases etc tied to your old Apple ID wouldn’t show up under the new one