Everyone seems to want to visit one now! What have I done? The 'st's and 'ct's are a kind of old typographic convention. I use them because I like old books and I think they look nifty, although I'm still a bit unsure about how well they sit with modern readers. Here's an example from an old type specimen where you can see some 'ct's. There are no 'st's because they used a long s back then. I'm ſane enough not to uſe long 's's on my webſite, though. I have ſome common ſenſe.
Haha, yes I think most readers would interpret them as fs rather than ſs. I assume you're using some sort of CSS to achieve the st's and ct's, right? I think old conventions like this are a good thing to revive, it raises a few eyebrows and gets people thinking about typography. That can only be a good thing.
I do like a bit of fancy typography. I'm not a typography dork, but I know enough to appreciate it. It's very exciting that CSS and Web browsers are mature enough to support typographical features like these - and it really is just flat text + CSS. You can copy and paste the text into a text editor and you'll see discrete letters instead of a single joined-up glyph or an image.