Editing the front page template
There are many possible ways to customize your front page content.

One of the easiest would be to create a view with page display and set the field order as you like and give a path to the view. Now you can change your frontpage to the path of this view (Configuration > Site Information - Default front page).

If you want to go with the standard front page and rearrange in the template as you described you could use drupal_is_front_page() to have different parts of the template for frontpage and other pages.