Sygate beats the pants off McAfee, Symantec, ZoneAlarm, Tiny, and a slew of others.
If you're on high-speed (broadband) Internet, you can expect a lot of portscans, probes, and other "scans." Most of these are harmless, unless your ports are hanging wide open.
There *should* be an option of some sort to limit the notifications you receive about portscans & such. Sometimes they're referred to as "silent" alerts, wherein they only show up in the logfiles, as opposed to popping up some sort of alert box.
If you don't have access to nmap, or don't know anyone who has it/knows how to use it/knows what it is, feel free to ask one of the *nix gurus for assistance.
...and don't bother with Gibson and his drivel...