What makes a good monitor:
Resolution : Resolution is the amount of pixels supported by a monitor. Typically the standard for gaming PC's is 1920x1080.
Response Time: There is always some delay between the video output from your PC to your monitor, however it is in the form of milliseconds. The lower the MS delay the better, especially for first person shooters. However, if you have to decide between 2 and 5 MS Delay time, there isn't much of a difference anyway.
Size: When it comes to size this is dependent in the eyes of the beholder.
LED vs LCD: A monitor equipped with LED Back-lighting makes it much brighter than an LCD monitor. LED monitors are also thinner. LCD's are pretty much the standard for monitors after surpassing CRT displays.
IPS: IPS monitors are known for their great color fidelity and viewing angles, however often result in a higher MS delay time. Typically they are used by video and/ or photo editor, but they can be utilized by a gamer as well.
TN : Monitors with a TN panel are basically the opposite of IPS panels, they have a really low delay time, usually 1 ms, but aren't the best at color and viewing angles.
Refresh Rate: Refresh Rate is the frequency with which a monitor's display is updated, the most common ones are 60hz, 120hz, and 144hz. The higher you go the better.
Personally, if I was you I would just save up about $100-$130 dollars and buy yourself a nice 1920x1080 22 or 23 inch display. However, if you do want to go cheaper you could always get something in the 1280x1024, 1366x768, or 1680x1050 department.