The way that I put posts inside static pages is like this:
Creat your categories. Then create the pages. You want to install the plugin Page Links To.
go to your live site, and click on the category that you wish to be in the page and copy the URL.
Go to the page and insert the link at the bottom of the page that says Page Link To and then publish.
When you click on the page, that should bring you to the category page with all of the posts in that category.