Your question looks straightforward but it is not so easy, indeed !
Ken Rockwell’s overview is quite exhaustive. Basically, AF-S and AF-I would be a good match for both your FE10 and your D5600. Most if not all AF-I are telezoom/telephoto. Furthermore, no AF-S with E, no AF-S with G of course would match your needs as they have no aperture ring. For ...
A full list of Nikon lenses which can auto-focus with the D5x00 line is available on Wikipedia at List of Nikon F-mount lenses with integrated autofocus motor.
The lenses with an aperture ring are those without a G in their designation.
So, for example, the first suitable lens in the list, under wide-angle primes, is the AF-S Nikkor 28mm f/1.4E ED.
Any kind of focus tracking ("AI focus" and the like) requires the camera to refocus between shots, and focusing requires the lens to be fully open.
Also, you can use your DoF test button with aperture set to something small (f/16..) to see how the image looks like when the diaphragm is closed, and you will observe that this is a lot dimmer than what you ...