Unable to see image on screen before taking picture only through viewfinder

That's the way this camera works. The D60 works as SLRs have worked for half a century. You view through the viewfinder, which views through the lens. The screen is for menus, setup, and image review, not for shooting. The LiveView feature, which turns your dSLR into a point&shoot camera, is a relatively new feature in dSLRs. Nikon introduced it into their lineup with the D3 and D300, and it took a while to trickle down to their entry-level dSLRs. While it's now in all their models, it's not in the three-year-old D60.

Sorry if that wasn't the answer you wanted to see, but there it is.