It's never a good idea to run two or more AntiVirus
programs because their different heuristics interfere with each others operation. I think Zone-Alarm Pro has both a firewall and an AV program right? If so I'd probably stick with Zone Alarm Pro rather than Avast!
EDIT: I see ZoneAlarm Pro is actually a firewall and anti-spyware with no AV, so it's best to keep both Avast and Zone Alarm unless you have any other AntiVirus program installed too.
Others will need to comment about the spyware software and popup blockers as I know zip about them.
"The great majority of mankind are satisfied with appearances, as though they were realities, and are often more influenced by the things that seem than by those that are." - Niccolo Machiavelli