If you're on Wordpress, install WP Supercache. That's 80% of the solution, right there. Install equivalent whole-page caching for any other framework or system and tell your HTTP server how to pick it up; that should leave you prepared for hundreds of RPS.
We're at the stage where people are posting the equivalent of "how I survived skipping lunch". It's not 1997 any more, tens of thousands of visits is a link from a moderately popular twitter account or a medium-size metropolitan newspaper.
I'm sorry to seem so uncharitable. I'm just not sure what value these posts add.