I agree that you should use a router (w/NAT) and run an up-to-date antivirus program. However, don't assume that all trojans and spyware will be detected by your antivirus software. You still need a software firewall to monitor outgoing connections. Your antivirus utility is not enough.
Nick,
In your case, when a trojan specifically targeted Zonealarm, it would be preferred to use Zonealarm pro or set a password so that the attack wouldn't be successful. Zonelarm and other firewalls are not meant to be replacements for your AV scanner. They should work together.
If you have these, you should be OK for "home" security:
1) Router w/ NAT
2) Software firewall
3) AV scanner
- occasionally run Ad-aware 6.0 or Spybot as well
~cdogg
"The secret to creativity is knowing how to hide your sources."
- A. Einstein