Unless you can move to a host quickly where you'll know exactly how your app can scale, I recommend you cache the hell out of everything possible. What does the site run on, by the way? Maybe we can offer more specific advice.
Anyway, ab (apache benchmark) is your friend. Hammer way. It might be that you don't even need any optimization at all.
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.