Increase the security...

If a people use a router with firewall and Avast (the best!) is necessary to us a personal firewall as ZA or Sygate to control the traffic outgoin?

Unless that Router with firewall provides outbound protection (some do via software), then yes you will need something to cover that function.

And ZA is a good solution? But if I use a personal firewall into a LAN with my router, I must configure something in za?

Whilst I don’t use ZA (or router, I’m on dial-up) I would have thought you wouldn’t have to change anything as the PC version of ZA is not providing network protection just for that PC.

I’m using ZA behind a router.

It will depend on your circumstances, we have 5 machines on the LAN behind the router and to allow communication between the machines and to avoid conflicts with the router itself some adjustments to ZA Trusted Zone were needed.

Well you do need a firewall no matter what connection your using, I’m using Zone Alarm and it’s best recommend if your new to Firewall configurations. Sygate is also great to have as well.