The following are performance characteristics:
Refresh Rate - 120Hz LCD monitors can display up to 120FPS assuming your CPU and more importantly your video cards can manage that. That's out of your price range.
Response Time - This is what most people look for. 2ms response time is considered ideal for gaming, but generally speaking 8ms is considered good enough. The lower the response time, the less likely you will see ghosting. However, response times is not a precise / absolute time and is highly manipulated by manufacturers. Basically it only represents the least amount of time it takes a pixel to change from one shade of color to another shade of color; the slowest times are all thrown out. Only the fast time is quoted. It's possible a LCD monitor will be rated at 2ms, but it's slowest time can be as high as 300ms while another monitor maybe rated at 5ms, but it's slowest time might be 250ms. Professional reviews really do not test the actual fastest time and slowest times of pixel performance since tests like this requires a lot of time, expensive monitoring instruments and a room with a highly controlled environment.
Input Lag - This is how much time it takes for a pixel to change color based on what you do. In games it affects how quickly it takes a monitor to display what commands you are sending via the keyboard and mouse (wheel, joystick, etc..). There is always some delay. It might be a low as 2ms or it might be as high a 40ms. Basically every 16.667ms equal 1 frame of lag assume there are 60 frames per second. So the higher the input lag the more time (or frames) passes before you actually see what happens on the screen. This spec is never advertised, it must be tested for in reviews, but it is very easily measured and generally does not need any expensive equipment other than your average camera; of course cameras with faster shutter times can give more accurate results. Most reviews usually covers input lag.
Quality measure or how well a monitor displays colors depends on the following (amongst other things as wells):
Color Depth - The greater the color depth, the more colors the monitor is capable of displaying; mainly known as color palette. All monitors are basically capable of displaying up to 16.7 million colors. Advanced professional monitors is capable displaying colors from a palette of over 1 billion colors, but only 16.7 million of them can be displayed at any one time. All inexpensive gaming monitors actually is only capable of displaying 256 thousand colors at the same time. Through a process called temporal dithering up to 16.7 million colors can be simulated by quickly flashing between two colors to make a 3rd color that the monitor cannot normally display. It flashes or pulses so that your brain thinks it is looking at a solid color. For example, pulsing between red and blue creates purple. All LCD monitors with TN panels and e-IPS panels does this. Only more expensive monitors (like $500+) can truly produce 16.7 million without using temporal dithering. Also sometimes known as Advanced Frame Rate Control.
Contrast - Generally speaking, the higher the value, the more capable the monitor will be able to display different shades of the same color. The true measure is Static Contrast Ratio which is generally up to 1000:1 for TN panel and e-IPS monitors, but TN panels generally exaggerates that figure a little bit. Another type of panel is VA which on average has roughly 3000:1 Static Contrast Ratio, but they generally have slow response times and are out of your budget. Manufacturers loves to advertise Dynamic Contrast Ratios which can be as high as 20,000,000:1 because generally bigger is better right? Basically Dynamic Contrast Ratio with a grain or maybe a pound of salt. Never truly trust it because it does not work the way you think it works. Basically Dynamic Contrast Ratio adjust the contrast ratio and to some extent the brightness of the screen based on what is being displayed on the screen. The darker the scene the higher the Dynamic Contrast Ratio becomes, the brighter the scene, the lower the Dynamic Contrast Ratio will be. I find this very annoying and I turn off this feature on my Asus VK246H monitor as well as my LG HDTV.