As a new user to Zonealarm you will find you will have several popups asking for permission to access the internet,if your surfing habits are genuine and stay away from the dodgy sites...allowing Zonealarm access should not cause you any problems.
Most of the firewall settings are set by default,so therefore can be trusted unless you would like to configure it to your own settings.
If you are unsure,post the requests from zonealarm and im sure someone here can advise you if to Deny or Allow.
Normally a little common sense and reading the destination will advise you if ok.
I normally block the ones with no IP address showing,but i got to admit...i dont get many of those.