If those problems show up, it usually is a sign of an inferior monitor. Serious graphic designers and game players will want at least 19 inches. The resolution is the number of pixels in the horizontal and vertical directions. The higher the resolution, the more information you can see on the screen at once, and in more detail. Higher refresh rates mean less flicker on the screen and less strain on the eye.
Refresh rate is irrelevant on LCDs, which are usually optimized for a fixed resolution.
Regardless of which size you choose, make sure your monitor is capable of at least 1024 X 768 resolution and a 75MHz refresh rate. The distance between the physical phosphors that make up a pixel, measured as a fraction of a millimeter. Again, this does not apply to LCD displays. In general, the smaller the pitch, the sharper the image. Look for a horizontal dot pitch of 0.25mm or less.