With Zone Alarm FW and Avast free, I think you will be fine. I would encourage MBAM (Malwarebytes-Antimalware) which is "on demand" protection but one of the best ways to remove malware and it's free. I would be comfortable with that set-up, and of course, always use common sense! Good luck!
On Jan. 1,2012 my free anti spyware/anti malware program (Counterspy) will no longer be available by itself. Will my free anti- virus program (Avast) be adequate to protect me? I am using the latest free version of Zone Alarm for my firewall.
Opinions and supporting details are welcome.