How to redirect after login, the working way?

You can use the WordPress function wp_redirect(). If you want a redirect after login or logout, check the plugin Adminimize, it has an option for this.

Two examples for a redirect in a custom plugin or functions.php of the theme (the following example uses the variable $pagenow):

function fb_redirect_1() {
    global $pagenow;

    if ( 'plugins.php' === $pagenow ) {
        if ( function_exists('admin_url') ) {
            wp_redirect( admin_url('edit-comments.php') );
        } else {
            wp_redirect( get_option('siteurl') . '/wp-admin/' . 'edit-comments.php' );
        }
    }
}
if ( is_admin() )
    add_action( 'admin_menu', 'fb_redirect_1' );

An alternative with $_server, checks the URL too:

function fb_redirect_2() {

    if ( preg_match('#wp-admin/?(index.php)?$#', $_SERVER['REQUEST_URI']) ) {
        if ( function_exists('admin_url') ) {
            wp_redirect( admin_url('edit-comments.php') );
        } else {
            wp_redirect( get_option('siteurl') . '/wp-admin/' . 'edit-comments.php' );
        }
    }
}
if ( is_admin() )
    add_action( 'admin_menu', 'fb_redirect_2' );