When you create a theme, you can use functions.php file for all utilize functions. Also this is the best place for all your require_once calls.
One trick I would like to recommend for theme development approach:
Don’t use direct require_one call to include your scripts. Instead of it, use locate_template function to load scripts. By using this function, all child themes will be able to override your scripts. So for instance, you have file called utilize.php, and it lies in inc folder of your theme, then instead of calling require_once 'inc/utilize.php';, call locate_template( 'inc/utilize.php', true, false );.
Now it will be possible to create inc/utilize.php file in a child theme and override parent file.