Supressing product display within a category is not really what the storefront module is designed to do (its primarily a product listing afterall!), and you can't display images along with category names without making code changes.

I would suggest that you get the source code running on your development machine (there are several posts here about how to do that) and then modify the category display yourself.

Just out of interest, why use images for the category links anyway?  If you're planning on using rendered text, then I think that visually impaired users would be more inconvenienced by not being able to resize the category name image (as they could do if it remained "real" text).  If you're planning to use images of products, etc rather than naming the categories with text then make sure you get your analogies right or users won't know where to click!!