Incoming links are very to your Search Engine ranking - this is very clear. The question is should I use "mywebsite.com" or "www.mywebsite.com<".

The answer: Either but not both.

Google, as an example, lets you declare a preference. What is important to point out is that Google and other search engines will treat the non-prefaced and “www” prefaced URLs differently. They will be treated as separate websites as you could technically have different content on each of those URLs. The idea of specifying a single URL also extends to mywebsite.com/index.html, www.mywebsite/index.php or any of the other variations. These varied website addresses will be indexed separately dividing your websites ranking.

In my opinion it is preferable to present a URL without the “www”. The URL is cleaner, provided less information for the viewer to process. The "www" is like a wall blocking the viewer from the important information - your name. However, it does not fully answer the question. In documents such as Microsoft Word use the full http://www.mywebsite.com. This rule would also be true for email content, not including the email signature.

Also, don't be concerned about whether people will understand if maywebsite.com is an address. ANYTHING with a .com is clearly understood as a website address.

Bottom line: In design pieces such as graphics, print ads, collateral material, DO NOT use the "www". For electronic documents and email, within content, use the http://www.