Hello marinos,
Sorry you're having trouble redirecting over www. It's hard to say what went wrong without knowing what specific errors you received.
When you re-installed your site, what did you set the WordPress Address (URL) and Site Address (URL) to be? If you set them as www during your re-install, you shouldn't need to change anything else in your WordPress settings. If not, you'll need to change that either through the dashboard or one of the methods outlined here:
http://codex.wordpress.org/Changing_The_Site_URL
(I usually find the wp-config.php method to be the easiest.)
I'm not completely familiar with how GoDaddy servers handle redirects, but I did find this information from their help center:
http://help.godaddy.com/article/5120
Take note of Step 7 in those instructions. You will want to set instances without www to be redirected. There's no need to redirect www back to itself and could cause a redirection loop.
It shouldn't be necessary to use both the redirect feature in your hosting account and the 301 simple redirects plugin. In fact, they could interfere with each other. Also, that plugin is really geared towards people who are migrating a site to WordPress and will not be keeping their same site structure.
Hope this helps!