Well, my response is vague mainly because I have not tried Norton lately, so I have no real world experience to give there. The Win2K reference is just for the purpose of a light comparison, being as the large bulk of Win2k users still left are running on a pretty strict "resource budget". As if to say, "If they can do it, why not you?". As for the hard facts as to the minimum hardware requirements, they are a Pentium 3 Processor, 128 MB RAM, 200 MB of free hard disk space. You probably know "minimum" means "barely crawling along", but your specs are well beyond those, I can't see you having any problems.
Weirdly enough, Avast!'s overall resource usage has actually dropped from older versions (4.8/5/6). Also, it has cache features to improve performance, so it will actually speed up (or rather, slow you down less) the longer it sits on your system.
There is one "netbook" problem that has happened before to some Avast! users, and will probably happen again....sometimes the maximized UI can be a bit to big for the screen, but not in any way that makes it unusable. Also, if you use a lot of little-known software (or make your own) the Autosandbox in ver. 7 might get on your nerves. Neither of those have much to do with your original concern, just a heads-up.