Tinycore is IMHO the best solution to squeeze the max out of an old rig. I run TC 3.4.1 on a Fujitsu Biblo B110, with similar specifications (PI-233MMX, 96MB RAM), and it works very well if you don`t use too heavy applications.
How much RAM do you have? Be sure to beef up to the maximum amount possible (AFAIK 144/160MB, by adding a 128MB module). Don`t worry about the Intel TX chipset`s L2 cache limitation, no workaround is necessary.
ACPI is problematic, but at least you can do a clean shutdown. APM would be better (with DSL/APM, suspend to RAM works for me), but no support yet.
A developer told us they will consider to include APM in a future release. Compiling it in by yourself is not trivial.
Opera is ok (but don`t expect flash, youtube and such things to work smooth). Besides Opera, I mostly use terminal applications.
You might need Xfbdev instead of xvesa.
If you don`t always need sound, load the drivers ondemand to speed up the boot sequence.
If you have some basic Linux knowledge (how to boot a kernel), no need to waste a CD-ROM, as Tinycore consists of just two files.
WLAN won`t run out of the box, you will need to install some few extensions, and your card has to be supported. Just try it (insert it and see dmesg).