In admin > Configuration > Layout Settings, set Categories - Always Show on Main Page to 1, and
Main Page - Opens with Category to 1 (or your category id).

You need a category to put your products in (ZC structural requrement), but in your case there is no point in displaying it, so you can safely turn off the categories sidebox in Tools > Layout Boxes Controller, as well as many other boxes.

To give more room for products, you may want to turn off one of the sidebars completely in Layout Settings (Column Left Status - Global or Column Right Status - Global). If you want to turn off both sidebars and move some necessary functions to the header, that will require some coding, but nothing that hasn't been discussed here already.