Enqueuing Script in functions.php vs on the page

Does it matter if I enqueue a script on just the page I need it to be used? As opposed to functions.php?

Or, what is the best practice? In this example I need a rotator just on the front page of my site.

And if I do enqueue it on the page, is there a best place to put it?

Go with functions.php.

Use the wp_enqueue_scripts action to call this function, or
admin_enqueue_scripts to call it on the admin side. Calling it outside
of an action can lead to problems. See #11526 for details.

Source: http://codex.wordpress.org/Function_Reference/wp_enqueue_script

function themename_load_js() {

    if ( is_admin() ) {
        return;
    }

    if is_page( 123) { // Replace 123 with your page's ID.
        wp_enqueue_script( 'jquery' );
        wp_enqueue_script( 'rotator-js', get_template_directory_uri() . '/js/rotator.js', array ( 'jquery' ) );
        wp_enqueue_script( 'rotator-init-js', get_template_directory_uri() . '/js/rotator-init.js', array ( 'jquery', 'rotator-js' ) );
    }
} 
add_action( 'wp_print_scripts', 'themename_load_js' );

Edit: Bonus tip: Whenever I need to do something like this, rather than hard coding the page ID in the function, I create an options page and add a call to wp_dropdown_pages() which allows the user to choose the special page. You said that you’re using the front page, so you could probably leverage is_front_page() within your function rather than checking the page ID, which is even cleaner.