I do have lots of experience personally and professionally on WWW and non-WWW websites.
I guess you have expertise in WP and SEO, so giving only main points to determine without explaining the story of SEO and WORDPRESS.
Lets consider the example scenario:
domain.com occupies 9 characters in the search engine URL data
www.domain.com occupies 12 characters in the search engine URL data (extra 3 characters)
if you are very much serious about SEO and wanted to rank and optimize your site for search engine traffic better to remove WWW in the website URL
Points to remember: 1. Inform google webmaster tools about your website (either www or non-www)
2. use .htaccess from www to non-www redirection
3. Use Wordpress Redirection plugin initially for monitoring what urls are being redirected and how
If you aware of Canonical URL concept, please go ahead and use properly
www.example.com
example.com/
www.example.com/index.html
example.com/index.php
Note: As you might be using Wordpress, using SEO Plugin will help you in applying a Canonial URL
When to use What - if you are looking for branding and not expecting too much search traffic use the extra WWW prefix
- if you are only interested to get search traffic and the website is not a brand (example: services, blog, keyword-rich domain) remove WWW
Consider Examples like:
moz.com
yoast.com