Changing a domain name

Changing a domain name

Hi,
I'm in the process of changing my domain name. My current mail is sara@mycurrentdomain.com and I need to change my mail to sara@mynewdomain.co.  If I change my current email to the new domain, will emails sent to my old address be forwarded to me?  If so, how do I change the domain of all of the emails in my account? 

Or is it a better bet to start over completely with the new domain and just set up email forwarding to the new domain?

Thank you!