Using a specific template for front page only

Well first of all it depends how you are enqueing your other scripts but make sure you dont add them before the jQuery library itself has been included.

There is nothing stopping you using conditional code in header.php to add scripts depending on the page that is loading, or even the template, category etc;

<?php

if ( is_home() || is_front_page() ) { ?>

// add your scripts in normal way

<?php } ?>