Curiously, the adoption of the 5.56 NATO round as the most common round type in America was rapid and overwhelming. But I don't think the same thing has happened in the handgun market. I presume that .38, 9mm, and .45 are all about equally common these days, with a significant number of .32, .357, and .44 running around, too.
Regardless, when the zombie apocalypse comes: maintain your calm, grab yourself something that shoots .5.56 NATO, and get on a sailboat out at sea.