Do Not Disturb is good for people who need the notifications, at least some of the time; but my emails are not important enough to interrupt me at any time; so I just changed the the New Mail sound to None under the Sounds settings.
You can go to the Notification Center settings, select Mail, and add a custom Alert Sound for individual accounts. This overrides the default Sound setting, making it possible to only receive alerts for only the accounts you care about.
I had one account like this. Past tense, I'm happy to point out.