Wow, yes, please get a MONITOR for gaming not an HDTV and one that is 1080p not 768p as the low resolution is problematic for many games in terms of visual fidelity.
You can of course run games at different resolutions on a monitor if need be due to hardware constraints (i.e. 1366x768 on 1080p monitor if necessary).
Unless on sale, TV mentioned is also $200USD.
Monitors have minimal input lag as they don't have video processing chips as the console or gaming PC does a good job of that already.
*Here's a 25", 2560x1440 monitor for $250USD if you can go that high:
https://pcpartpicker.com/product/D7hj4D/acer-monitor-umkg7aa002
That's way, way better. If too expensive there are other choices (see pcpartpicker). I'd look for:
1) IPS panel (can just select IPS to filter out in pcpartpicker-> monitor)
2) quality/reviews (i.e. customer feedback at Newegg)
3) resolution (at least 1920x1080)
4) screen size (at least 23" recommended)
5) Video input (HDMI, DP, DVI as needed from console or gaming PC)
6) *Audio passthrough is important if you have a game console. Want a headphone jack or any audio output such as RCA (red/white) to connect to desktop speakers or else you'd have to find speakers that can connect to the game console some other way.