the eBay link didn't work so I can only see your pictures. unless you left a picture out, it would appear that the monitor doesn't have a VGA input, one cable has a composite input, S-video input, and component inputs. the other cable has three RCA connectors (either an A/V input or an A/V output). is there a third cable with a VGA input?
if it has no VGA input then the picture will look like crap no matter how you hook it up. of the available inputs, component would have the best picture but its unlikely that your video card would have a component video output. S-video is the next best, and composite is the worst. you can use them for a front end, but they are all incapable of displaying the small text that normal PC programs use.
I also assume there is no touchscreen on that monitor? what will you be using as your input source (mouse, trackball, touchpad, etc)?