How to change the URL of a clickable banner?

I recommend you register a post type called ‘header_slide’ and use the featured image of said posts as the banner. Do a query with a maximum of 1 post per page and display the banner, and add the url as a custom field.

Something similar to this:

$q = new WP_Query(array(
    'post_type' => 'header_slide',
    'posts_per_page' => 1,
    'orderby ' => 'rand'
));

if($q->have_posts()){
    while($q->have_posts()){
        $q->the_post();
        if(has_post_thumbnail()){
            $url = get_post_meta($post->ID,'custom_header_link',true);
            if(empty($url)){
                $url = home_url();
            }
            echo '<a href="'.$url.'">';
            the_post_thumbnail(array(920,200)); // adjust numbers to fit desired size
            echo '</a>';
        }
    }
} else {
    // hmm no header slides were found, ABORT!!!!!! or maybe display a default
}

wp_reset_postdata();

To generate the code for registering the header_slide post type, go here:

http://themergency.com/generators/wordpress-custom-post-types/

Answer the questions and it will generate a chunk of code for you at the end, put that code into your themes functions.php, and make sure it supports custom fields and featured images/post thumbnails