If you own a web domain, you can set up several email accounts such as yourname@yourcompany.com. If you do not have a web site you generally will have an email account with your ISP provider. In that case your email would be yourname@yourispname.com or yourname@yourispname.net. There are also other Internet Companies that provide free email services such as yahoo, msn and google.
I would advise having one personal email account. This would be the address you would give to friends and family for jokes and pictures of your kids, etc. Do not use this one for business purposes.
I would suggest having a second email for non-family and non-business purposes. Often if you need to purchase something on the internet or download software you will be asked for confirmation with an email address. Unfortunately, this will get your name on several databases that can then be used for sending you unsolicited email i.e. Spam. By having this extra account, you will not be loading up your valuable email accounts with extra messages.
Finally, I would have a business email. The name should sound professional, be easy to remember, and relate to the business you are in. I have received resumes and other business correspondence that referred me to email the sender at iluvbunnies@aol.com or istopforbikers@hotmail.com. This does not leave a great impression.