You’re right–Norton is a poor choice, one of the poorest available.
For an anti-virus program, I recommend eSet NOD32, if you are willing to pay for it. If you want a free anti-virus, I recommend one (do not run more than one) of the following three:
Microsoft Security Essentials
You also need anti-spyware software (even if you run a program like Microsoft Security Essentials, with anti-spyware capability built into it). I recommend that you download and install (freeware) MalwareBytes AntiMalware