It's running on PHP 5 in a shared hosting env (Dreamhost).
The framework is homegrown, but pretty small. PDO is used as an abstraction later talking to MySQL. It uses Smarty for templating.
If it's your Wordpress site that you are worried about, Wordpress has a caching plugin that is supposed to work if you can get it installed properly.
Both of those are file-based caches.
If you want to get super ghetto, save a copy of the loaded page that is going to be hit the most and rewrite the URL to that saved static page.
Since we're talking about a podcast here, the traffic is most likely going to be distributed over time, so you really shouldn't have to worry that much.
Anyway, ab (apache benchmark) is your friend. Hammer way. It might be that you don't even need any optimization at all.