Wordpress with no caching plugin on a $5-a-month droplet, that's what. It's a pleasant enough platform to use, but if you don't cache content and you make the HN frontpage, you're gonna have a bad time.
Probably. You can also use a VPS for more things than just Wordpress, and shared web hosting tends to be kind of a crapshoot in any case; if you're up to doing sysadmin work, you really are better off with a VPS, not least because someone else's screwup is a lot less likely to impact your site.
Any experience how many users you get from the front page? I guess there are a lot more clicks than comments, so it could've been 10k-100k?
Should of course still be no problem for any server that serves cached content, but somehow that number of requests brings down a fair amount of frontpage posts..