Buy a nice TV
Give it a static IP
Firewall it off from the internet
Voila!
Edit: Make sure it cant call UPNP on your router or any such tomfoolery
If you really want a true dumb TV, you should look into the commercial TVs
Personally I just get any TV and don't connect it to the internet. I disable any popup interfaces/home menus as much as I can on the TV so I just turn it on and it goes to HDMI1 and that is all the TV's interface needs to do.
I also disable alot of the picture altering features as well. My LG TV has some true motion crap that just made everything a little bit off.
For the most part the handful of TVs I have tried just work.
I'd search an used and old one if i was you
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Linux is a family of open source Unix-like operating systems based on the Linux kernel, an operating system kernel first released on September 17, 1991 by Linus Torvalds. Linux is typically packaged in a Linux distribution (or distro for short).
Distributions include the Linux kernel and supporting system software and libraries, many of which are provided by the GNU Project. Many Linux distributions use the word "Linux" in their name, but the Free Software Foundation uses the name GNU/Linux to emphasize the importance of GNU software, causing some controversy.
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