Well, today I uninstalled Norton Internet Security and replaced it with ZoneAlarm pro and Avg - the ones I have been using until now on my other computers.
The reasons:
1. Norton reported finding tracking cookies, but was unable to fix the porblem, leaving "Ignore" as the only alternative. OK, these are not the most dangerous threats, but I didn't like it.
2. I've tried running complete scans twice, on both occasons the software crashed.
So my experience wasn't entirely positive. AVG/ZoneAlarm are probably not the best software, but they are the ones I'm used to. And so far I've been happy with them.
BTW: The new PC works like a dream (and by that I don't mean a nightmare!).