Once you setup a hosting account for your new website then you will need to point the domain name to this new host. The following link will taek you to the page that will show you how to edit the namecheap and godaddy nameservers.
You can setup your gmail account to send and receive emails from your websites email address. So firstname.lastname@example.org can be rouited to email@example.com
One of the main benefits is that you can then access your email from any computer with an internet connection. Click on the link below to see how.