10.4 is probably the safest compromise if you absolutely must run OS X on that hardware.
A newer G4 would be better for OS X, a G5 or an early Intel Mac would, ultimately, be better still and still have HFS read/write compatibility under 10.4 and 10.5.
10.5 has full HFS read/write, and slightly less good AppleTalk compatibility.
(Remember: largely networking is your best bet here.)
10.5 won't run out of the box on your G3/G4 configuration, but if you get a G4 CPU, you can trick it. It's not generally worth it, though.
What sites are you browsing? Netscape 4.8, WaMCoM Mozilla 1.3.1 or Classilla [most recent version] will run fine and be good for most sites explicitly offering vintage Mac downloads - (in particular, Macintosh Garden).
Regarding filesystem: 8.0 or 8.1 and newer (I forget which) can boot HFS+ on PPC machines, but that version can also use HFS+ data partitions on 68k.
So, ultimately, if you do something like:
1)buy a literally brand new iMac or MacBook from the apple store in downtown Portland
2) buy a SCSI2SD v5.1 - store.inertialcomputing.com/SCSI2SD-V5-1-p/scsi2sd-v5.1.htm (you can get it with a db25 port to use externally)
3) buy a big SD card
4) run 8.1 on your CC
5) format the SD card HFS+ using 8.1 on your CC
6) you can now move the SD card between the scsi2sd in your vintage mac and a USB card reader in your modern one
While you're booted in system 7 or older, you'll only be able to use plain HFS volumes this way, but you could run a big HFS volume on a SCSI2SD and use OS X on 10.5 or older to be able to write to the volume.
you can just put the SD card from the SCSI2SD, and you'll have the fastest possible computer compatible with a filesystem your vintage Mac can use and suitable for preserving resource forks when transferring data.
(I actually recommend using networking rather than doing all of that, but the point is that it *is* possible.)
This kind of hearkens back to a comment I made in the previous thread about not really needing a bridge Mac given that your CC's got an '040 and a bunch of RAM and OS 8 on it, and can load Macintosh Garden in Netscape 4.08.