I run a few big sites on WordPress, and would totally recommend you use the simply static plugin, and configure nginx to serve those cached files directly so it never hits php. I also usually put cloudflare in front as well, but you can have a screaming fast wordpress site that scales really far by itself without it just with that trick.
If you need some dynamism, w3 total cache is also a great choice.
Check out this thread for recommendations on static site generator plugins on top of Wordpress. Best of both worlds for folks who want high-level publishing.
