I had the bright idea to dig through Reflector to see where the Focusable property is used, and found my way to this solution. I just need to add the following code to my Window's constructor:
Loaded += (sender, e) => MoveFocus(new TraversalRequest(FocusNavigationDirection.First));
This will automatically select the first control in the tab order, so it's a general solution that should be able to be dropped into any window and Just Work.