If you just want to have your own email address at your own domain, I don't think I would set up a mail server for that. By doing that your computer has to be on and connected 24/7 plus you just opened up your personal computer to every kind of hack and things like that. Not that linux can't handle it but it would be alot of trouble just to have a different email address.
Most isp's give out there own email address's like my isp is TBSCC and so my email address there is
marcus@tbscc.com you could probably get an email with them and then just set up one of the many fine email clients on your linux machine to read the email.
Or you could buy your own domain sort of what you mentioned above I think and have it hosted somewhere and then use the email from where you get it hosted.
Or if you want I have a domain threadaweb.com if you want an email at there give me a yell I will make you one, you can check it with an email client or I have squirrelmail there too.
So many options out there for you, take your pick