Configuration Settings of Authcache + File Cache
After testing for several settings, I came up with the following configuration:

$conf['cache_backends'][] = 'sites/all/modules/filecache/filecache.inc';
$conf['cache_default_class'] = 'DrupalFileCache';
$conf['filecache_directory'] = '/var/www/clients/client1/web8/tmp';
$conf['cache_class_cache_authcache_key'] = 'DrupalFileCache';

$conf['authcache_builtin_cache_without_database'] = TRUE;

$conf['page_compression'] = 1;

$conf['page_cache_maximum_age'] = 600;

$conf['cache_backends'][] = 'sites/all/modules/authcache/authcache.cache.inc';
$conf['cache_backends'][] = 'sites/all/modules/authcache/modules/authcache_builtin/authcache_builtin.cache.inc';


I am using nginx and just change the $conf['cache_class_cache_page'] to $conf['cache_default_class']. I don't know if I am using the correct config, but this works for me.

And the speed of my server increase significantly when I ab test it.