What firewall are you using, out of interest? AVG AntiVirus is a good package generally, but it does not include a firewall.
If you're running WindowsXP or Vista, the built-in firewall should be sufficient providing, as Chuck said, you're fairly cautious. Make sure that it's enabled though, because if it's not it won't do you any good whatsoever.
When you say your firewall is telling you that you don't have browsing security, I assume you're actually talking about AVG's pop-up that occurs when it updates (using free version). This is just what's called a "Nag Screen" whereby they're trying to get you to upgrade to a paid version to feel safer. If that's the case, ignore it and just continue as usual, there's little more that it will offer you (save for not nagging you anymore).