I have Outlook setup so that an envelope appears in the system tray whenever an email arrives. However, most of these emails are from mailing list which I file off automatically and mark as read - however, the envelope still appears. When I ran the same setup in Thunderbird, the envelope did not appear if I setup a rule to mark these messages as "read".

Any ideas of how I can set this up in Outlook?

From the dealings I have had with both Outlook and Thunderbird I really would recommend sticking with Thunderbird, as I run Firefox perhaps I'm a tad biased but I do believe it to be the better software.
Saying that, I run a web based email client so it's really no answer I know.
POP3 advocates please step forward.

Yes, I would agree with you: I only use Outlook as I need it (I think) to be able to sync my PC to my PDA... I'd go with FF and TB every time, otherwise.

But having said that someone must have written something to sync non-Microsoft programs with a PDA. I still like the interconnectedness of Outlook but I'm open to suggestions... (I'm switching my second laptop to Linux soon and it would be interesting to see if that could sync with my PDA)