Hey there @qriouslad!
I'm running a WordPress/WooCommerce website create with EasyEngine --wpfc (fastcgi_cache) and I've managed to get a really high performance website having W3TC enabled. The only issue though is that when W3TC plugin is enabled, the WordPress backend gets terribly slow.
By the way, I'm using EE recommended settings for W3TC https://easyengine.io/wordpress-nginx/tutorials/single-site/w3-total-cache/ + some minor tweaks on my own, please see it here
Perhaps I'm missing something in order to make the WordPress backend more responsive. @rexi88 have mentioned that caching the database might decrease performance in some server instances. I'll check this out somewhere else.
Anyway, W3TC allows object and page caching, which can really enhance the website's performance in terms of caching, thus improving its loading time and all other benefits that comes with it.