Welcome to the world of wireless networking!
What you describe seems pretty typical, I have exactly the same thing happen with the wireless connection to my laptop. It just seems to drop at odd times but then picks itself up and reconnects after a few minutes. Leave the router firewall on and Zone Alarm if you have it but turn off the Windows Firewall. Make sure Zone Alarm is also turned off for your network, just disabling the firewall does not disable it for networking.
Hope this helps.