When it comes to online shooter games, all of these factors affects ur perfomance
- FPS: Yes, definitely,higher fps allows faster reflect Couple with high refresh rate is the way to go if you are competitive type of gamer
- Latency: Yes, it prevents unregistered hit, delay, rubberbanding.
- Input lag: most of gaming monitor, mouse,keyboard have low input. It's probably not as important as the above. \
- High refresh rate: allows you see things clearer, less blurry so it helps your vision in fast paced shooter.
A simple method to test how high refresh rate and low input lag: https://www.humanbenchmark.com/tests/reactiontime
Try 10 times, click as fast as possbile in 2 diff setup: 60Hz, normal mouse vs 100/144/240Hz gaming monitor, gaming mouse
In my case, my result is clearly faster when i do this test. One from my office computer , one from my gaming PC.
Lol, I reacted 50ms faster with the gaming PC.