Displaying the most recent post on the front page of my website

Is the index of your “static” website a .php file (i.e. index.php)?

It is, so as to accommodate little bits of PHP like includes.

In that case it’s easy: you have several choices.
1. Follow this tutorial, especially Scenario #1:
https://www.transycan.net/blogtest/2005/07/05/integrate/
2. Make your main index.php “WP aware” (the method is described in the guide linked above) and use any recent_posts plugin; install, activate and then put the call into your index.php. (For an example for this latter solution click on my name here and under Services look at the sidebar on the right)

Thanks for that – it includes the titles, but I’d like to put in the content of the actual post. Can it do that too?

With my first suggestion – yes.

It works! Cheers mate.