Change admin defaults for reading settings

You can use the wpmu_new_blog action to automatically set the default to 6 for new installs:

function wpse_139900_default_posts_per_page( $blog_id ) {
    update_blog_option( $blog_id, 'posts_per_page', 6 );
}

add_action( 'wpmu_new_blog', 'wpse_139900_default_posts_per_page' );

If you don’t want your users to be able to change this setting, you can just override it instead:

function wpse_139900_posts_per_page() {
    return 6;
}

add_filter( 'pre_option_posts_per_page', 'wpse_139900_posts_per_page' );

Either way, you should never use your own query on top of the default loop – it’s just unnecessary overhead that can be avoided by tweaking the main query.