Adding icons to posts via checkboxes?

I’m working on a blog about ice cream parlors in my city, and I’d like to be able to have a panel of checkboxes on the Edit Post page that, when checked, add an icon to the post. For instance, check off Ice Cream Cakes, Milkshakes, and Frozen Yogurt, and have those three icons appear in the post’s designated area for icons. It would be nice if people could also sort the posts by what icons they have, but I don’t think I want to use categories for this as they’re already sorted into categories by area. I’m also wary of using the tag system for this, because I’ll probably need to add tags which don’t correspond to the forms of ice cream served.

Any ideas how I can best accomplish this?

Thanks,
Michelle