LP
To have a personalised domain name in your address you really need to own and manage the domain name. To register a domain can be free and a search in google should return you plenty of results.
With respect to the email, you will need some form of email service running on the domain and this usually requires a hosting package so you have disk space to store emails as and when they arrive.
So it may cost but my domain costs for the year including hosting cost about $50 a year so it's not a major expense.
Hope this is of some use!!
z..