Hello mikeb,
Welcome to a great board and a great cart. Let me address your questions: These three sections will show products on your home page in under the different titles.
The Latest Products show up when you add new products - they are automatically shown by the date added.
The Featured Products are controlled by the FEATURED check box within the Product edit page, it's the second field, the one just below the on/off
The Specials are also controlled from with the Product edit section - after you add a product, the section is Promotions
which has two areas, one for quantity discounts , second of for specials (sales) that's what turns on the Sale tag, and displays in the Specials section on Home page.
Here is the link the the documentation that will give you details about the entire Product area.
It's is recommended that new cart users read the documentation - it will really help your understanding of the cart.
http://www.abantecart.com/ecommerce-documentation/31-admin-user-manual/catalog-menu/productsLee