In your prior or current position, would you have used your personal email address for customer communication on behalf of your company?
On your CV, an email address like "email@example.com", "firstname.lastname@example.org" or "email@example.com" is not likely to leave a favorable first impression. It should go without saying, yet...
Treat your job hunt email like company communication.
P.S.: Don't waste time by obsessively checking your web mail account for responses. Have them automatically forwarded to your smartphone.
Do you need help with sharpening your professional profile online? Talk to your personal Career Adviser!