Question about second monitor for competitive gaming

[Exhjil]

So i already have a really good setup 4090, i9 13900k but the thing is that, i use a lg c2 42" as a monitor, and its insane. But, i can feel the input delay of the monitor, when i play with competitive games ( valorant, fortnite, lol ) and even on normal everyday use, but its okay since i dont care when i play with stuff like cp2077 or smh. So i think about buying a second monitor just to play this games on it, and the big question is, should i buy 360hz or 240? the price diff is there, and keep in mind that i only plan to use it for mainly these 3 games. I found MSI G27C4X / this monitor, its a 250hz 1ms monitor, and seems to be good for why i want it, but i cant find any normal review about it any info? should i pay more and buy a better one, or is a monitor in this price category is okay? i dont want to throw out money, so if a cheaper one wouldnt work
And i found stuff saying that the lg c2 handle true 1 ms response, while most of the monitors just say that are 1ms, and i cant really understand how is this true? . ( i upgraded the firmware, put the settings to the correct ones, turned off gsync etc. but i can feel the delay )
Looking for a honest advice.
(sorry for my English its not my mother language.)

 

[Regeneration]

Set your LG C2 to PC mode (edit inputs) and then put it in game mode (in color presets).

In the PC make sure its set to full RGB and 120hz. If you still feel lag input, try lowering the resolution, but you still get input delay, then nothing can be done.

All HDTVs are laggy in first person shooters and thats why its better to stick to a PC monitor.

If you want to buy another monitor just for gaming, highest refresh rate the better! but anything above 144hz is good. 240 or 360 doesn't matter much.

Just make sure the monitor is "1ms GTG" and not 1ms fake bullshit. 2ms GTG is also good.