Though it really doesn't matter, for a "professional" website having www. at the beginning does tend to look a bit more authentic. Though that probably has to do with the fact that it has been used for years.
Heinlein quote signature? Extra points. Er, point.
It's best to build a brand around the "clean" version, but you kind of have to make sure that www points to you as well because of people who look a lot like me. (What little hair I have left is... well, "grey" is being charitable. It's more "white with a couple of stray darker hairs in the mix if you look really closely".)
There was a time, back when 500 MB was a bigger hard drive than most people could afford, a top-of-the-line machine had 32 MB of RAM and 14.4 Kbps was a high-speed connection you couldn't count on, that a company's web server (www.example.com) would have been just one of the machines you were likely to deal with. Ten years ago, if you typed "example" into your browser's address bar, a nifty new feature would automatically put "http://www." in front of it and ".com" after it. People my age were trained to automatically add "www" to every URL they see, and not everybody keeps up with the changing world. If your target audience is under 30 years old, you'll probably never need to use "www", but if there is anyone older and not tech-savvy, then you need to handle "www" as well. Just don't make it your brand; typing "www" is annoying when you don't have to do it.