there is absolutely no technical reason for adding www to your website. Its your choice to go with or without www because many popular websites with www like google, facebook. These websites redirect
http://google.com to http://www.google.com
Also there are many websites without www like twitter, stackoverflow.com. These redirect
http://www.stackoverflow.com to http://stackoverflow.com
I think you can choose to add or omit www
One important point to note that
You should have a permanent redirect rule to redirect from
http://www.twitter.com to http://twitter.com
This is because if you have show the content for both www.twitter.com and twitter.com
Your search engine ranking would be split into two halves instead of twitter.com having 1000 ranks
http://www.twitter.com would have 500 Ranks
http://twitter.com would have 500 ranks this spoils the popularity of the website.
Btw Search engines would understand the redirect rule.