If at all possible upgrade your RAM to at least 128MB. That much RAM allows so much more - a PII really isn't all that bad, even if the videos are a little limited.
If that's not possible, you definitely want a pre-existing swap partition prior to installation.
Another possibility is AntiX:
Based on the current version of MEPIS 7 , "Lysistrata", using Debian repositories, and compiled to allow use of PIIs, (although PII MMX may not boot), it allows use of a modern kernel and repositories on a low end computer. "Spartacus", based on the 6.5 version of MEPIS, using older Ubuntu repositories is recommended for PII MMX, AMD K5, and AMD K6, and older cpus.
I use AntiX "Lysistrata" on my IBM Thinkpad 570 - a PII 366, 192MB, 6GB notebook. The first GB has Win2K installed for drivers, and a few astronomy programs with no linux equivalents that run under WINE. I chose to use the full distro ~310MB that includes AMI PRO, an excellent word processor, and even added on KSTARS - without installing the full bloat of KDE. The same can be said of Gramps genealogy software. However, there is a base distro of ~ 178MB. "For those who wish to have control over the install, use antiX-base."
There are so many more choices available with a debian based distro - my notebook is far more useful than before, and very easy to configure to my taste. I have tried all the distros you listed and more, including tinyme, yet, for reasons of appearance, useabilty, software availability, speed, etc... AntiX has been the best compromise for this old beast.
"The default windows manager for antiX is fluxbox. It is a very light, fast and flexible windows manager."
As a branch of MEPIS AntiX has it's own forum:
but many questions will have answers similar to those of MEPIS: