Knoppix certainly would do all that you ask, and then some.
However, something small and easy would be DSL (DamnSmallLinux).
DSL uses 50MB on a CD, preferably a business card size CD because that's cool, but any CD will do.
It runs Live and can be persistent or run from a USB pendrive. The forum support at www.damnsmalllinux.org is great, in contrast to others we may or may not frequent.
Give it a look.