I'd recommend Avast for your virus protection...
http://www.avast.com/
Download the home edition - registration is required, but free!
As for firewalls, I've been perfectly happy with the built-in XP/Vista firewall, so I wouldn't know what to get there
I'd also recommend running Spybot Search & Destroy every so often to clean up any spyware, ads, etc. that may have accumulated on your machine.
http://www.safer-networking.org/en/index.html
Remove Norton for good? Well, if add/remove programs doesn't do the trick, I suppose you could search the registry, but I'm not sure what exactly to look for... heck, maybe Spybot might consider Norton to be spyware now if it's really that hard to remove!