What versions of Linux (or UNIX) are good on old 486 boxes?

Going through stuff on the shelf and I've run across a couple of 486-based fully-integrated LCD/touchscreen machines. One is a SCAN Corporation SCANtouch Model 3000, the other is a Planar Systems box. Similarities include limited memory (2x 72-pin SIMM sockets on the SCANtouch or 4x 30-pin SIMM sockets on the Planar, both with "double-sided SIMM" support, so 64MB or 32MB max respectively), one ISA socket (no PCI), onboard NE2000, serial, parallel, 2.5" PATA disk... these systems will run MS-DOS, of course, and Win95 (the touch screen on the SCANtouch is old enough that it apparently doesn't work with Win98 mouse drivers, according to forum posts I dug up). I really don't care about running DOS or Win95 on a touchscreen/LCD machine