BasicLinux is designed specifically for old PCs. It uses a small kernel and busybox to provide a low-RAM Linux, capable of browsing the web, doing email, and functioning as an X terminal.
The current release of BasicLinux is particularly suitable for old laptops -- it has PCMCIA capability and includes MagicPoint (a presentation tool similar to PowerPoint).
The current release of BasicLinux is 3.32. BasicLinux comes in two versions: one boots from a DOS harddrive, the other boots from floppies. Both versions have the option to install themselves to a Linux partition on the harddrive.
BasicLinux has a slim IDE kernel and a small set of common modules. If you need a more capable kernel and/or additional kernel modules, you should get them from Slackware 7.1. You will find kernels in the /kernels directory and modules in the /modules directory.