Every Android-based media player I've had tried just plain sucks, the NVIDIA Shield wasn't too bad but at some point the controller quit charging. You can still get a game console with a built-in Blu-Ray player too and it's nice to have one box that does that as well as being an overpowered for streaming.
I have a HDHomeRun hooked up to a small antenna pointed at Syracuse which does pretty well except for ABC, sometimes I think about going up on the roof and pointing the small one at Binghamton and pointing a large one at Syracuse but I am not watching as much OTA as I used to. It's nice though being able to watch OTA TV on either TV, any computer, tablets, phones, as well as the Plex Pass paying for the metadata for a really good DVR side-by-side with all my other media.
As for TVs I go to the local reuse center and get what catches my eye, my "monitor" I am using right now is a curved Samsung 55 inch, I just brought home a plasma that was $45 because I always wanted a plasma. I went through a long phase where people just kept dropping off cheap TVs at my home, some of which I really appreciated (a Vizio that was beautifully value engineered) and some of which sucked. [1]
[1] ... like back in the 1980s everybody was afraid someone would break into your home and take your TV but for me it is the other way around