Making a custom template match up to created page?

Hi, Noobish here. What I’m trying to do is create a front page that list only posts in the Front Page category. I have other post categories set up, and will have special pages for those. What I did was to create a New Page in the Admin, called it Front Page (front-page). I have installed a post from category plugin that seem to do the job of selecting the posts via a short code. And, I also set the “Front Page” page as the front page in the site settings.

What I’m confused about is what template is this page using. I assume it is the index page. I would like to create a custom template for the front page, but I’m not finding how to associate the Front Page to a front page template. Any replies would be appreciated.