That's a though one. I personally like Mozilla better, because it looks so much like Netscape, which is the shit (well, used to be, Netscape sucks now-days).
Firebird got some fixes Mozilla doesn't have, like not showing a WMV file as ASCII.
I guess you should try Mozilla first, because it's at version 1.6 (which is stable) while Firefox is at version 0.8 (which means not finished).
If you find Mozilla too hard, try Firefox.
About the e-mail:
Mozilla got a built-in Mail client.
Thunderbird is a stand-alone mail application, which you should use in combination with Firefox.
[ February 25, 2004: Message edited by: Refalm ]