My current setup is that I have an Echo Dot connected by the line out to my A/V receiver, with the microphone turned off. With Spotify Connect the Spotify on my computer or phone can tell the Spotify on the Dot to play a song, album, or playlist. The Spotify on the Dot then streams that music from Spotify. I can turn the computer or phone off and the music keeps playing. Spotify on my computer or phone will show what is playing on the Dot and let me control it.
This works really well. (In fact, it works way better than Amazon Music from my computer or phone works with the Dot. I just finished a 90 day free trial of Amazon Music and one of the reasons I did not subscribe was how poorly Amazon Music works with Echo devices. Spotify completely blows Amazon out of the water there).
What I really like with this is that once I start playback the computer or phone no longer needs to be involved.
I know that there is an Apple Music app for Echo that lets Apple Music be a source for Echo, so that I could say "Play Foo on Apple Music" and Alexa would use Apple Music do do that, but I don't want to choose my music by voice. I want to do the choosing on my Mac or phone/tablet.