This is something I've been mulling over for awhile. Obviously every character is different, and presents different challenges for the editor and cover artist(s).
The Atom, for example, is tiny. So Julius Schwartz had Gil Kane create covers which presented the Atom in a difficult situation, often precisely because he was so small:
With the Flash, at first the covers emphasized his incredible speed, as in the famed cover to Showcase #4:
But there are limits to that approach, and so Schwartz and Carmine Infantino began emphasizing his colorful villains:
With Green Lantern, Schwartz and Kane went more with puzzle covers. How can this be happening, and how can GL get out of this situation?