From what I can tell the story covers/thumbnails resize probably based on a css property. Could we have built in crop preview on the site for story covers? I have just been guessing when I crop before uploading. A set of sizing guidelines and best practices might also help. Like what are the breakpoints for the sizing on the images, min vs max width and all that.
From what I can tell you need to make it a perfect square for it to appear properly on the front page. To long across and the sides get cut off so no wallpapers unless the image is perfectly closed captioned so to speak. If you use portrait pictures the top and bottoms get cut off. It all depends on where the shorter edges are.
Images get saved in different sizes for different purposes. (I think "original", 300x300 and 160x160) Some of them like the preview picture get resized and cropped to square format.