How to load javascript file on homepage in WordPress in order?

In your functions.php:
edit: First register the quicktags script under a different name than already registered in wp “quicktags” , see Codex

function quicktags_script() {
    wp_register_script( 'quicktags-min', '/wp-includes/js/quicktags.min.js?ver=3.5.1','','',true);
    wp_enqueue_script( 'quicktags-min' );
}

add_action( 'wp_enqueue_scripts', 'quicktags_script' );

This will load the script for all the pages on your front-end.
To load it only on front-page :

function quicktags_script() {
    if(is_front_page()){
        wp_register_script( 'quicktags-min', '/wp-includes/js/quicktags.min.js?ver=3.5.1','','',true);
        wp_enqueue_script( 'quicktags-min' );
    }
}

add_action( 'wp_enqueue_scripts', 'quicktags_script' );

Just add the last parameter $in_footer for the wp_register_script to true (see the edited answer) . Or add ‘quicktags-min’ as the third parameter for the basicktags register function

wp_register_script( 'basic-comment-quicktags', '/wp-content/plugins/basic-comment-quicktags/quicktags.js','quicktags-min' );

This will first load quicktags-min and then the basictags.