post ordering question

Use a custom field named 'order' in each post. Remove the field from posts you do not want to display. Then call the WP_Query object to sort the order field numerically (meta_value_num) skipping any values less or equal to 0 (like in the meta_query below).

$posts = new WP_Query( array(
    'orderby'    => 'meta_value_num',
    'meta_key'   => 'order',
    'order'      => 'ASC',
    'meta_query' => array(
        array(
            'key'     => 'order',
            'value'   => 0,
            'compare' => '>',
        ),
    ),
) );

if ( $posts->have_posts() ) {
    echo '<ul>';
    while ( $posts->have_posts() ) {
        $posts->the_post();
        printf( '<li><a href="https://wordpress.stackexchange.com/questions/118725/%s">%s (%s)</a></li>', get_permalink(), get_the_title(), get_post_meta( get_the_ID(), 'order', true ) );
    }
    echo '</ul>';
}

wp_reset_postdata();

In this example, the number in parenthesis in each link is the value in the 'order' custom field.