Which caching option is best - FastCGI? Does this mean I don't need PHP-FPM?
--wpredis is currently the best
Does the basic setup have PHP memcache?
The setup with W3TC use memcache, but redis is better than memcached.
Is Varnish needed as well as FastCGI?
With Redis, Varnish is not needed : Why Redis is better
If I use FastCGI, will I need a WP plugin like SuperCache?
For each caching system, a WordPress plugin will be automatically installed.
And what miminum size Digital Ocean droplet is recommended for this type of install. I currently have a $10/m size.
A $10/m droplet is enough