When Face the Occasion asked for a mobile and tablet version of the desktop website I built for them, I was able to make it happen in less than two hours using what I mentioned is my favorite way to make WordPress sites mobile-friendly.

Drop-down menu that comes with all theme options in WPTouch Pro.
After analyzing the situation, I went with WPTouch Pro, and in a very short time had a wonderfully functioning site on smaller devices. I hand-built a responsive landing page, and left the rest up to the plugin. The theme comes with a hamburger menu in the top-right which list all the pages (accept for any that you remove) and loads everything fast.
Done.