I did use Varnish before but removed it because it just did not behave predictable on mu Nginx running VPS. Too many little issues (can't even remember what exactly) and could not afford to keep on monitoring different clients sites on the multi-site WordPress platform and iron out each issue (which might result in another popping up elsewhere) so I decided to remove it again... Too bad because the speed was a real advantage :(
I had the opportunity to test Lightspeed for a short while and it seemed to behave much better with WordPressMS out of the box but sadly, the licence is not something I can afford.
Recently, I've added WP Super Cache in PHP mode (the default mode but not the fastest) to my WPMS running on Nginx/PHP-FPM and it is blazing fast too. So I'm happy again :)
Anyway, I responded on your new thread to the issue at hand.