I wouldn't worry about the number of shots taken by the body. They're good for hundreds of thousands. There are a few things I would watch out for though.
Check the lenses very carefully looking for any imperfections/scratches. Hooke each one up to the body and look through them very carefully. Note any spots. Hook up another lens and see if there are spots in the same place. If there is, it's an issue with the body.
Look at the mirror and look for debris. If it gets junk on it, it will have to be cleaned. Most people just take it to a shop to be cleaned. The D60 will have an anti-static feature, but dust and crap still clings to the mirror.
Make sure the AutoFocus works. The Nikon has motors in each lens, while the Canon will have one motor in the body. Turn off the AF. Turn each lens to make sure it focuses correctly and there is no grittiness in it.
Turn the lens to zoom in and out and make sure it is smooth and not gritty.
Obviously look for any damage to the body, particularly the LCD screen and corners. Dents/scratches in the corners mean it was likely dropped.
The D60 is an awesome camera, and is what I have. However, my friends D40 cost a little less. The D40 has basically the same features. His camera can take pictures more rapidly without having to stop and wait for the camera to write the pictures to the card.