In reply to Michael.

For ESI, there is a module - https://github.com/pintsized/ledge . Our launchpad build doesn't have it but.

We use fastcgi_cache for simple content websites where writers/site-admins are only logged in users. For membership-site or bbpress forums, where logged in users percentage is higher, memcache-based object-cache and database-cache (using a plugin like W3 Total Cache) is good choice.

Using HHVM can speed up things so much that you will stop wondering about other caching mechanism! Only downside is, hhvm doesn't like all WordPress plugins, so it is recommended to use FPM as backup php-interpreter. Reference - https://github.com/rtCamp/easyengine/wiki/HHVM-with-EE-2.x.x#use-hhvm-and-adding-php5-fpm-as-fallback