Of course you need firewall installed along with your antivirus.
I was Sygate user and I never had any problems with Sygate and avast! working together. Of course, everything that Sygate asks you regarding giving permissions to avast!, withouth any doubt, all those question related to avast! permission, just give permission. You have to do that in order to let your avast! works fine.
Cheers !
EDIT: btw, if Sygate is too complicated for you, why don't you try with ZoneAlarm. Easiest firewall to set up ever. It works great with avast! installed, no problems at all... be sure (always) that you completely uninstalled previous firewall prior installing new one. Same story with antiviruses... never install another antivirus untill you completely removed the old one. That includes cleaning some registry keys as well...