If you wish to use a custom URL for your email address, you will need to create an MX record in your DNS settings. You'll need to follow the instructions provided by the email host to create the appropriate MX record in your DNS settings.
Learn how to Create an MX record.
If you do not want to use the email hosting provided by your domain registrar or email hosting is not provided, you have a couple of options.
Zoho Mail provides 5GBs of mail storage on their free plan. Most users will need a single email account, but the free plan with Zoho allows for you to register up to 5 accounts.
Google Business Apps offers 30GB of mail storage per account at $5 per month per account.