I would suggest a mini-PC running Linux and Plasma Bigscreen instead of an AppleTV if you want something 100% private and user-controlled.
Unless you're using streaming services like Netflix, in which case you're stuck with 720p because of widevine.
Do you recommend any specific distro for this?
my priority for a TV isn't privacy or user control, it's minimizing annoyance. and appletv, roku, or similar streaming boxes delivers that best.