The eyes should be bright, clear, and big, not sunken.
The gills of a whole fish should be bright and red, not dark and dried out looking.
The flesh should be firm, moist, and elastic. It should not leave an indentation when you press it.
The skin on a fish should be moist and viscous. The natural “slimy” coating on the skin of a fin fish is actually a good thing and a sign of a very fresh fish; it helps to keep the fish from drying out and extends its shelf life a bit. Wash it off before cooking.