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
SpywareBlaster 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
IE-Spyad, which, as explained on its home page, " ... adds a long list of sites and domains associated with known advertisers, marketers, and crapware pushers to the Restricted sites zone of Internet Explorer. Once you merge this list of sites and domains into the Registry, the web sites for these companies will not be able to use cookies, ActiveX controls, Java applets, or scripting to compromise your privacy or your PC while you surf the Net. Nor will they be able to use your browser to push unwanted pop-ups, cookies, or auto-installing programs on your PC."
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.