Can someone please provide a simple explanation on how to decide whether to try the 486 or 686 version of Antix 8.5? I would be MOST grateful, particularly if someone posted an answer that I could understand. (Written on a very old Thinkpad running Lysistrata).

Very old processors like Pentium I and AMD K5 and K6 are an older architecture than i686, which was introduced with Pentium Pro. They need a kernel compatible for them, the 486. All other CPU's can use the 686.
For more modern CPUs (AMD x64 and Some Pentium IV and beyond) there's the amd64 compatible kernel (not in antiX). Any CPU can use a kernel built for an earlier architecture but not for a newer.

Thanks a lot. Much appreciated.