[Full-Disclosure] A rather newbie question

If someone could take a quick look through my log file - it is very simple and shows a bazillion requests that are being bounced off my firewall. I would really appreciate it. My ISP didn't care and didn't respond when I let him know about all this traffic that was wasting MY bandwidth. And then they were upset when I nmapped back to a few addresses and hit some upstream providers router - oh well, live and learn. They told me they would terminate my contract if I kept that up. Hey I was just trying to find out who the freaks were that are constantly attacking MY network.
Anyway, what I am looking for is confirmation that even though I may be new - I am not losing my brains or paranoid, thanks.
I have updated all my systems to the latest patch version - but I'll tell you, it is the users inside the firewall that cause the most problems. All our machines have antivirus, all have antispyware, but they are used by my kids and sometimes their friends, and therein lies the problem, but hanging out in the background with you guys has opened my eyes to the craziness out there. How is a "normal" citizen supposed to keep their computer safe on the Internet? I don't think it is possible.

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