How do I listen to my iTunes playlists on the apple tv

I think this is what your asking:

iTunes Music Home Sharing - Listen to music files via AppleTV “Computers” App from PC

I'm only familiar with my setup via ATV 4K. Maybe it's the same for all Gen's of ATV's?

1. Open "iTunes" on PC.
2. Click on "File" and Turn On "HomeSharing" (enter email & pw). Note: iTunes on PC must remain open but you can be minimized while using. You can closeout your iTunes library when your done but I recommend staying connect to HomeSharing.
3. Sometimes it's necessary to Authorize your PC. If so, Open Accounts/Authorizations/Authorize this computer.
4. On AppleTV select "Computers" App.
5. On Apple TV select “Shuffle All” or “Song/Artist/Album" etc. and begin play back.

Tip: There are more options for play back I can share with you if your connected to a Receiver (via Airplay).

Tip: Once connected to HomeSharing (again, I'm speaking what is available via ATV 4K) you can share your music album art (except for compilation albums) via screensaver on your TV. There a lot of visually effects to choose from.

Also, if your interested, there is a "Remote" iTunes App for your iPhone to listen to your iTunes music from your PC. It involves a little more navigation & setup on your iPhone.

Hope this is the info you are asking for.

What ATV Gen do you have?

Yes, I am doing the same. I have very few purchased songs but about 300 cd's that I have copied into itunes. It should play them all back bu your selection of choice.

At the top of your ATV screen does the work music appear? If so, click on it.

That's Great. I'm glad it worked for you. Happy to help. Thanks Bob

You need to select the App called Computers (it's Orange in color). Not the Apple Music App.