If you remove Norton and install AVG, you will be pleasantly surprised at how much faster your PC runs. McAfee is more like Norton than is is like AVG.
The free firewall from ZoneAlarm is the way to go. It takes a while to get fully set up (every time anything tries to communicate with your PC or the internet, it asks you whether or not to allow it).
If you have a modem/router, it may include a NAT firewall. I would still use ZoneAlarm too, just to be sure.
A spyware scan is a good thing to run. A virus scan is essential. AVG does my machine every morning at 0600 while I'm elsewhere.