If its Norton Internet Security you oughtta be fine, Vivien, as long as its updated frequently and properly configured. You prolly should consider some anti-spyware/anti adware stuff, just to be safe.
IMO, the basics for safe surfing include the following, all free:
Spybot Search & Destroy
(read the Tutorial
and the FAQ
to learn how to properly update and configure Spybot S&D). Spybot not only scans for and removes a buncha yuckware, it can and should be configured to prevent the crap from installing itself. Included are several very useful utilities, including a Startup Manager and a Registry Monitor/Lock.
Recommended by Spybot S&D's developer, JavaCool's
is a valuable adjunct to Spybot; the two of them work well together. Spyware Blaster targets and locks out thousands of known yuckware pushers.
Also highly recommended is LavaSoft's Ad-Aware SE
. AdAware Free does a good job of finding and removing adware, and some other yuckware, though the free version does not offer real-time blocking. Its a good idea to scan your system regularly both with Spybot and AdAware, as one will often catch something the other misses. Consider them a team.
Rounding out the basic protection suite is
With that kit, properly configured and updated, along with likewise properly configured and updated anti-virus and firewall, and a little common sense, you're gonna be about as safe out there on The 'Net as you can make yourself.
And I'm sure I speak on berhalf of the other "techies" when I say yer perfecwy weccum, wabbit. We're all glad to help where we can.