Note that there are (a very limited number) monitors with a 240Hz refresh rate and the monitors available are expensive, i.e.; >$500 USD.
The thing is, the human eye can see as many fps as the system/game can generate. However, the brain is only capable of perceiving some or most of all of those images. A system/game could be putting out 200fps, but your brain will cut out most of the images because it is simply too much information for the brain to process into a fluid picture for your to perceive. Say a system/game is putting out 200fps and is showing images of an enemy running and gunning for you. Your eye will see all 200fps being generated, but your brain will only process some of those images providing they are similar enough to form a cohesive image for you to perceive.
Let's suppose 200fps and let's take just 5 of those images as still shots, if the 3rd image out of the 5 of the enemy running and gunning was missing his helmet and boots, your eye would see all 5 images but your brain would not process the image with the missing boots and helmet because it was not similar enough to the images before and after to allow you to perceive the missing boots and helmet. You may, on some imperceptible level, think something was wrong, but you will not be able to explain what or why. With that said, there is a significant difference between what your eyes can see and what your brain will process into images that you can perceive.
But to answer your question, with a budget of $200USD, just buy the monitor with the biggest screen size at the maximum resolution with the quickest response time your $200 will buy; which will most likely be a 23" or 24" LED backlit LCD with a max resolution of 1920x1080. Like this one...
ASUS VX248H Black 24" 1ms (GTG) HDMI Widescreen LED Backlight LCD Monitor.
Hope this helps. Good luck!