How to create a theme that handle articles in different categories?
You will want to create different content types for each type article.

I would then use Views and Panels to create the page. Create a view for each subset of article types then place each view in your panels page.

You could also do it with a theme by creating what panels creates for you but you would still need a view with a block setting and then places the views block in the correct section of your site and set the block to only show on the home page. 

The views+panels is a much cleaner implementation that is theme independent.