I’m using the latest posts for my frontpage, and I can’t seem to find where’s the file at. I use Custom Template and created base-custom-template.php and replace some div class;
The home page set up during activation is static and it doesn’t use the custom template. You also want to display the latest posts, so you don’t need a page template anyway.
If you consult the codex you’ll see you need a new template called front-page.php (it’s showing posts so start by duplicating index.php). You can then create a new base file called base-front-page.php and editing that to how you want it.