Unfortunately, White Box is not actively maintained (looks like abandoned)...
Some other options could be: Fedora (not sure if it supports 486), Ubuntu -
http://www.ubuntu.com/ (and Kubuntu) and Slackware - http://www.slackware.com/.
Ubuntu is a nice alternative for home users. If I had to do with a 486, probably I would
begin with this, if Fedora did not work.