Just be careful with what you download (zip & exe files are often infected)... scan everything that you download with your AV before you open it.
I don't use Norton, so I can't comment, but a few forum regulars do & are happy with it. Whatever AV you choose to use, make sure that you keep it updated.

Have a good read through this thread, it's full of tips & advice
WARNING: Viruses on the network you should be aware of


If you do get into trouble, or just want your computer checked out this is a really good (free) site Norbiesworld