it's not a preference actually (like if the web was based on personal preferences)

Google is checking first if a mysite.com exists... if not, www.mysite.com is checked out and then google say it's impossible to find.

your server is supposed to manage www. calls, so it redirect to your site in the /public_html/ path. if you have no /www/ ALIAS directory below your /public_html/, ou can ask your webmaster to make one... (it's simply a alias of the /public_html/ path!)

.htaccess files are not handling the situation very well, just replacing the www. but that cause a sub-domain to be used and your site may have cookies problems if it is done.