@ a vast lover
I haven't tested Avast! with Private Firewall much, but AIUI they run pretty well acceptably together, but PFW isn't one of my top tier three free FW program choices. (That's not to say that it isn't Dr Ron Paul for you though!)
My 3 top tier free FWs are Comodo, Online Armour & Outpost.
My second, middle band tier programs that run successfully enough better than Windows are Private Firewall, PC Tool's FW (adware) and 'Windows 7 Firewall Control' which actually just uses the OS default much better than how Microsoft has it, with intuitive outbound control.
Also even with free Avast! and a free 3rd party FW I still recommend to use free versions of MBAM and SAS anti-malware/spyware.
Zone Alarm doesn't function compatibly with Avast! AV and also inserts itself into your browsers, so I advise avoiding it altogether.