Thinking about these five elements can teach you a lot about color in Web design. You want a subtle but noticeable color, distinct but not heavily saturated. There may be a half dozen if you count Institutional Green. As we note below, the six-cubed palette leaves much to be desired. Generally, avoid dark colors, whose numbers are all at the low end of the scale.
Pastels can weigh heavily on the eye.
Beiges are nice, but try to find one. Obviously, this color must contrast effectively with the background color, especially if you put lots of words on your pages as we tend to do. It should probably be darker than the background rather than lighter, though there are always exceptions. You'll need to balance lightness against mass. This is where things really start to get complicated, since the link colors need to coordinate with both body text and background.