As I recall, the K6-2 lacked one hardware instruction needed to allow
it to run on i686-optimized code, and my perception is that a lot of
modern distros are optimized for 686 or better. I believe you will need
a distro built for a 586/486/386.
I can't really comment beyond Slackware (my distro of choice), which
comes with a 486-optimized kernel that should run on your system readily. I
run it on a P133, and even an old 486, but I never leave the command line
with them. 512M of RAM might be necessary for the internet these days,
but I'd give the current RAM a shot first, maybe add a big swap
partition, see if it is tolerable. A not-too-oldish nVidia video card in a
PCI might allow you to offload video decoding of, say, YouTube videos as
well. An old 8400 or something.
I believe some of the BSDs come 386-optimized as well. OpenBSD, FreeBSD,
NetBSD, or DragonflyBSD might be worth looking at, if you can't get no
Linux satisfaction.
--
Slackware 13.1, 2.6.33.4-smp, Core i7 920
GeForce GT520, RLU #272755