Hi TomSwift. I don't know the exact minimum specs of them, but to suit your needs it might be worth checking out:
Damn Small Linux
Puppy Linux
or
Feather Linux
(no particular order)
All are designed to run very light-weight on systems that would probably choke and die running most modern OS's.
As far as I know all three have the option of running Firefox and Thunderbird (most of them come with Firefox installed as the default browser).
Have a look and hopefully you'll find something there you can use.