Should I use www?
The short answer is, it doesn't really matter, as long as you're consistent and forward the alternative to your main domain.
If you'd like to know more about the background to this question, read on. The subdomain www is a subdomain of the highest level of your site, e.g. for the domain example.com it is the full domain www.example.com. Historically www was used for websites, and other subdomains might be used for other purposes (for example mail. for a mail server or ftp. for an ftp server), in practice nowadays most websites serve on both www and the bare domain, and www is somewhat redundant. Browsers like safari now omit the www when quoting the domain in the address bar, and many prominent sites use the bare domain (twitter.com for example), so the www seems to be slowly dropping away.
As with every question on the internet, you can find someone with an opinion on either side, in fact people have even registered domains about this - www.no-www.org and yes-www.org in order to wage holy war about the lack or not of www.
You should always choose one domain for your website to live on, and redirect from any other domains to that domain. This is known as the canonical url, and also applies to content on your site - you should not serve the same content on several different urls - instead choose the one you wish to be the canonical url and redirect other content to it.
So whichever version of your website you choose - www or bare domain, you should always redirect from the other to your preferred name. This lets users use either www or the bare domain when visiting your site without problems. People *will* link to the wrong version of your url, so be sure to handle it and redirect to the one you prefer.
“Canonicalization” is a big word that Google may or may not have made up to refer to “the process of picking the best URL when there are several choices.” No matter which format you decide to use, the important thing is to be consistent and help search engines determine the “canonical version” (ie. the version that best represents your entire site).