yes - is the quick answer...
Software? Very much down to personal preference, I'd recommend the one built into Mozilla, or maybe the Firefox thunderbird, plenty of people happy enough with Outlook Express if you want to go with the M$ herd though.
Before all that though you'll need to register your domain (joebloggs.com in your example) and, by the sounds of it, you are going to need to read up on POP3 and SMTP which are the two components to that....
If you want an easier introduction to the mechanics of it that you can do right away sign up for a web based email account like Yahoo! and they have the option to configure it for POP3.
Ask more specific questions and you'll get more specific answers as you go along, but, like I said, the answer is yes!