To me, someone with a hotmail account is a student, one with a gmail account is a step up but still not arrived;, when I see an aol.com account it looks like the person hasn't kept up to date. Even when I see someone with a web site and then a gmail account I'm assuming that they haven't been in the business very long. Not a signal you want to be sending out there. You need to look established from day-one, there is no gradually entering the industry, the moment you start searching for work you need a web site and email address that match up. Keep the gmail accounts for personal business, but make sure your business email reinforces your name and establishes you as a resource.
I've also seen the gamut of email addresses and web site names that all lead to confusion and many times are not only hard to remember but also difficult to type in when you're trying to contact them. Using email@example.com is not a way to market your work as an illustrator. You've got to imagine an art director trying to remember who was that person we used three or six months ago on a project, the supposed catchy name will never replace a real name—the name that goes on the purchase order, your invoice and on the check that goes out. Make it easy, just keep it dead-simple.
And always have your web site on every email—hyperlinked so it's dead-easy to get there—and your phone number, never send out an email without several ways for someone to reach you, no matter who you're sending to. It's so easy to setup a standard signature in Mail, you can even select typefaces for a custom look. We get a ton of mail here from illustrators who just give us their email address; no url, no phone number and I suspect their doing it with every email. That's no way to promote yourself—no way to grow your business.