Had it not been for Cloudflare, I am not sure my server could have handled that. Before I did that, I set up Varnish as a cache provider for users who are not logged in. That is effectively the second line of defence now.
The server itself is a dedicated server at Hetzner. I use the server for a bunch of other things, that see nowhere near the same activity as the Infosphere, and I also use it for my personal screen+irssi setup. But all in all, the server costs me about 50 euros a month.
Though, again, Cloudflare is basically the single most important reason it's not costing me more, and why I have not needed to hand it over.