I've been a hiring manager for a Fortune 100 company, and I've hired for my own company, and for other people. I also hire contractors and consultants.
A gmail account is fine. Some variation of first.last@ or f.last@ or what-have-you is all good. When gmail first came out, it was viewed as the mark of someone in the know, especially on the technical side. Now, not nearly as much, but it's still fully acceptable.
There are many serious consultants with gmail addresses.
Yahoo is a bit less OK. I mean, it's got "yahoo" right in the address.
AOL brings up the back of the pack. "You've got a rejection letter."