Janet,
In the article contents on your home page, or through a Custom HTML module, add the following tag:
{SCOpenGraph image=http://site.com/link-to-image.jpg}That will instruct Facebook what image to use on that page (you can do this on any page you want).
Additionally, in the Social -> Open Graph area of JFBConnect, you can set defaults for pages that haven't been explicitly set (or aren't pulled by JFBConnect automatically). It's good to set defaults for things like your logo, so Facebook doesn't have to guess at the best image for your page.
Hope that helps, but if you have any questions, just let us know.
Thanks,
Alex