New, quality, name brand monitors are so cheap that it doesn't make sense to me to buy a used one. For example, I just looked at the monitors available at Costco's online web site and there is a $90 LG and a $110 Dell. Both are 24" monitors with HD resolution and 2 year warranties. I presume that you are not a gamer or someone who edits high resolution video. If so, either of these monitors should be completely satisfactory for you and exceed any specs you need.

Make sure the video output of your new computer matches that of the monitor, or you can get a cable to match.