If you are using the default template then the content of the centre section of the screen is defined by the page :
www.yourdomain/zen-cart/includes/languages/english/html_includes/classic/define_page_2.php
This will be the case for when a user first reaches your Zen-Cart web-site and is effectively the Home Page.
When the user picks a category though, if it is a bottom level category, then the products will automatically display in the centre section for that category unless you get someone to so some programming to do a re-direct. It is normal though that when a user picks on a bottom-level category the products will display.
If however you want the above but don't like the higher level categories displaying content in place of the Home Page then one way you could stop this happening is to modify slightly the code page at :
www.yourdomain/zen-cart/includes/templates/template_default/sideboxes/tpl_categories.php such as to make the higher level categories static and non-links. I have example of this page if you want + site in operation (but it won't include your icons etc)