I use a computer monitor as a television. It has speakers, but doesn't have a remote. I'm wondering if the nexus player or other android tv box would work well with this. Does android tv have built in volume control that works through HDMI or Bluetooth speakers? Does android tv send a sleep signal to the monitor, or cut the video feed? My dish box goes to a screen saver when you turn it "off" so the monitor doesn't go to sleep.
I can't answer all your questions but I can answer some.
It doesn't have built in volume control unless you run something like Kodi on the box.
The nexus player never turns off, it goes into a low power state and keeps a video signal active to your TV and thus wont allow it to sleep.
It may just be best buying a universal remote for the monitor?
On the Shield TV, the controller it comes with has volume control (the - and + buttons at the bottom of it), and it goes into a chromecast style screen saver after a while of inactivity. Also it has IR so you could use a harmony remote with it. Not sure about the sleep signal though.
As mentioned the Shield TV has volume control builtin and volume control on the remote.
If your monitor has a sleep function (power off after n minutes) then that is probably the best way to get it to power off automatically, but you'll have to set it manually.
I have a shield Android TV and have been using it with a computer monitor for the last 36 hours, it have volume control on the gamepad and the remote, and you can tell the unit to sleep and the monitor will shut off