First find a program to monitor your FPS in-game. (MSI Afterburner, Fraps etc.)
Secondly, i would recommend using native TV's resolution and find what FPS you're getting. (Do not forget to turn off VSync, because it locks your FPS). If you think the gameplay is not smooth enough, lower down the settings, turn off shadows (or make them lowest) and reduce Anti-Aliasing - lowering these two settings will increase your fps by a lot. Is it now smooth enough? If you hit more than 60fps, you can make your settings better and increase the quality, you just have find your own golden middle place between quality and smoothness.
Well if the gameplay is at native resolution and lowest preset and you still want it to be smoother, then lowering the resolution will increase the FPS drastically, but again it depends (i would like to know the resolution of your TV and your GPU model), If that TV is 4K, lower it to 1080p, if your TV is 1080p, lower it to 900p, 768p or 720p depending on your needs. But first, before reducing screens resolution you should check in-game settings, they usually have a setting called "Resolution scaling", so when it's at 100%, it is rendering games at your native resolution, make it lower to 90, 80, 70.. etc. so you don't have to play with screens settings and again, test your system and its capabilities until you find the best place between the quality and smoothness you find good for you to play at.
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