Glad you got it sorted out, but to answer your original question:
1) The front-page.php template file, if it exists, will be used to generate Front Page content, whether the Front Page is set to display the blog posts index or a static Page.
2) The home.php template file, if it exists, will be used to generate the blog posts Index, whether the blog posts index is displayed on the Front Page or on another static Page. (Note: front-page.php has priority over home.php for the Front Page.)
3) If neither of these template files exist, then index.php is used to generate the blog posts index, whether the blog posts index is displayed on the Front Page or on another static Page.