Adaware is a great product but not the end all to be all. I also use Spybot Search & Destroy (available free @ CNET Doanload.com). Spybot is a great program and better than Adaware in that it has an "Immunize" feature that blocks the bad stuff BEFORE it can creep into your PC. Bottom line is that each Adaware & Spybot seem to pick up a few items the other misses.
As far as firewalls go, any firewall worth its salt requires some configuration because folks have different stuff programmed & installed on their PC. ZoneAlarm is a good product. Those "pop-ups" are allowing you to configure the firewall on a per occurrance basis. Be sure to check the "remember this setting" box when you respond to its annoying behavior that is trying to help protect you. While many firewall permission requests are legitimate for programs you have installed on your PC, if you have many different files asking for permission to transmit data out of your PC with cryptic names that don't appear to correspond to known software or Windows, then I would be concerned that you have alot of tracking cookies or other spyware trying to send intelligencia back to their minions.
Personally, I prefer McAfee Internet Security Suite which contains anti-virus, firewall, and privacy service. It's not free, however, worth the $$ in my "been using personal computers for 25 years" opinion. After using Symantec Norton products for many years, I found them difficult to upgrade and virtually impossible to uninstall without editing the Windows Registry. Life is difficult enough without having to deal with poorly written and supported software.