I'm using a theme that has it's own home page layout but I want to use a normal page instead. I can't find a way to change it because in Settings> Reading, the home page is already set to 'Home' (a page which already exists for my mobile theme). It seems like the desktop theme home page is just overriding this setting.
I think this is the best place where you should look when it comes to handling with templates for different type of pages you using.
So for the main index page the
front-page.php is the first one which WordPress will look for.