Do you have an old PC lying around gathering dust? How about a small-capacity USB flash drive sitting, unloved in a drawer? You can reuse your old computer and a USB flash drive by installing a tiny Linux distribution.
Mini Linux distros are great as they require fewer system resources than other options yet still deliver a whole operating system experience, and we have nine of the smallest Linux distros for you to choose from.
Honestly, just use Debian. It can run under 200MB of RAM (default install), so it beats all distros on the list except for TinyCore and SliTaz, and it actually has packages.
Indeed was my first thought when I didn’t see on the list.
Chrunchbang or Bunsen are exactly this, vanilla Debian with stuff set up with openbox. The vast majority of ppl don’t need anything more lightweight than this. (maybe conky should be removed, but that’s it.)
If the old PC in question is a small laptop, such as an EEEpc, then I would use vanilla Debian with i3, because I really would want tiling on that…