I know a lot of people who have gone to the effort of getting a website but still use gmail or their internet provider for their business email account. If you are paying to register a domain name and to host a website, be sure you also get your own email address.
I have several email addresses. People can send email to me as Mike Becvar, Sir Toony Van Dukes, or Balloons By Mike. They could also send me email to my account with gmail or Verizon. Part of the magic is that all of the messages end up at the same place, my email inbox. I have configured my website to forward email messages to a single account. I have that account configured so I can send email messages under any of those names.
I think it looks a lot more professional to tell people my email address is Mike-[at]-BalloonsByMike-[dot]-com instead of some generic name like Mike-[dot]-Becvar-[at]-Verizon. I am also much less likely to need to change my email address if I move or change Internet provider.
Check with your website hosting account to see if you can setup your own custom email account and check with your current email account for settings that will allow you to send and recieve emails from multiple addresses.