I play on a 4K TV. I tried playing at 4K resolution for a while, but found that I prefer a stable high framerate, so play in 1440p on it, instead.

Personally, I think it's a very fun experience if you have a CPU and GPU that can handle it. I prefer as big of a screen as possible, it's one of the few benefits of a flat panel over a CRT display.

Don't worry about what monitor elitists may say. TV response time is getting better and better, and there are now OLED TVs specifically designed to run games. And even without, the input lag isn't that noticeable.
If one cares about sheer quality of display, regardless of size, they would be better off using a CRT display rather than a flat panel to begin with. It seems rather pointless to me to focus on the importance of an ultimate display instead of size a TV provides, and then advocate or flat panel PC monitor instead of a Cathode Ray Tube.

It's a good idea to read up about which monitors have a good degree of response for gaming. And I apologize that I don't know what the best in the $400 range would be. But flat panel TVs are generally getting better for gaming.
My friend has a LG CX and swears by its quality. But it is quite a bit more more expensive than $400.