Norton was a 'pig' on slow computers of the time frame you mentioned. It worked 'OK' on faster machines then, but not the low end ones. By worked I mean it didn't bog you down and KNOW it was running. Today, well, both its engine is much better, probably core and thread driven, and of course, computers are faster, more powerful, and have more RAM. However, that 6 year old computer would probably still have a problem even with today's version. I would think anyone with a fast, 3Ghz or faster P4, or any duo-core or higher with enough RAM so the OS they are running doesn't swap would be fine with today's version.
Thunderbird, well I like it because I KEEP my e-mail on my computer, not on a server somewhere. I started using it eon's ago, when Outlook was barebones as an e-mail client and I never liked IE and used Netscape which also had an e-mail client. The Outlook that shipped with Windows wasn't as good as TB, but in later years the Outlook that came with the Office Suite was probably just as good. TB of course has many add-ons that you can use. Eudora which is no longer being updated or possibly supported is probably just as good too. Use what you like, but if you think your present e-mail client had short-comings, try TB. A desktop e-mail client is better than ANY Web based client.