Considering the leaps and bounds the linux kernel has progressed since the 2.4 series kernel I would seriously avoid it for performance reasons doing something the OP mentioned like web browsing.

The Damn Small Linux project is dead; there hasn't been a release in 3 years. One of the primary developers is now working on Tiny Core Linux. Tiny Core sounds like a good fit for the OP; its extension system fits the description "a packaging system built around single-shot apps".