1GB Ram is not that much for a server that uses apache + mail and FTP server. Also the speed of the system depends on how many other vm's are running on the same hardware node, e.g. if the Harddisk IO is high because there are many other vm's running on the same node, then you might get problems like you described.
To protect your server against being overloaded, you can install mod_evasive.
To speed up php processes, ensure that you use php mode php-fpm or php-fastcgi and not cgi or suphp and install a php binary cache like apc or xcache.