Can’t select "My Photos" for screensaver

Since I just bought a new generation ATV and had the same problem, here's my solve:

1. Under Accounts > iCloud: if you are signed in, turn OFF iCloud Photo Library. Then a "My Photo Stream" option appears (I assume you need to have this feature enabled on your phone, etc). Turn ON.

2. Return to General > Screensaver: now when you select My Photos, you should see as the first option under "My Albums," the option "Photo Stream." When you select it a new window appears and in the upper right you will find a "Set as Screensaver" button!

Photo Stream is a good option if you don't want to manually change picture albums for your screensaver, as it automatically updates as your photo stream updates. Take a picture with your phone - moments later it's on your TV screen!

Screensavers have never had the ability to auto update, the ATV caches a select group of photos and if you want new photos you need to cache a new batch.

With the latest version of TVOS you can now see nested folders and use them for the screensaver (as well as slideshows).

On earlier Apple TV's the screensaver set up was more intuitive and allowed you to see always-updating recent pictures without having to create and manually update a shared folder. Any way to do that now?

Again, screensaver doesn't auto update. The photo stream itself will update with the latest pictures, but that's also the case with iCloud photo library (with ATV now supporting nested folders and ability for screensaver/slideshow across all albums)

Could you clarify how you are making these selection in full, if I understand you correctly, I'm simply unable to replicate your experience.

You can only select shared albums for the screensaver

Yes. For shared albums you will see the option in the top right to set as a screensaver. If you want you can give feedback. Just be aware that the screensaver would only use a small amount of space for caching, typically only 100 photos are used

http://www.apple.com/feedback/

If you have iCloud photo sharing enabled then you go into the shared album on the ATV and you have to navigate to the top right to set the screensaver.

You are trying in the wrong place, but you don't have to start creating shared albums you can still use your regular photo albums.

You can select your albums for the screensaver from your computer via homesharing. It doesn't matter if your computer isn't connected regularly, it copies a number of photos to the Apple TV internal drive and uses them in the absence of a connection when you run the screensaver.

How to set up Apple TV screensaver with photos from your computer

http://www.idownloadblog.com/2015/12/10/how-to-apple-tv-screensaver-computer-pho tos/

I do not have a computer anymore. Just 2 iPads and 2 iPhones.

I do have an iMac 5K in my office.

Is there another way to use my icloud photos for the screensaver?

If you are using iCloud then there's no computer involved, you just need to use a shared album as outlined above