2. Install MorphOS (I managed to boot from a DVD, so this proves it's compatible)
This is your best option. OS X will be completely unsupported on this machine - Apple seem to pretend that PowerPC Macs don't exist any more.
3. Install AmigaOS 4 (NOT 4.1) using an ISO file I downloaded tonight which says it uses the loader Moana and will install onto a Mac Mini G4. I don't know if my Power Mac G4 is compatible.
Best advice here: forget it. Moana is not complete, and wouldn't work anyway. It was abandoned when it was decided to stick to new hardware for OS4 so that it wasn't tied to obsolete hardware and technologies (but please let's not argue about the pro's and con's of that decision in this thread as it's OT and done to death already).
4. Install Yellow Dog Linux
5. Install Free BSD for Power PC
What's the point? It'd just be an underpowered, incompatible version of what you can run on any old PC.
What do you think I should do with it and why?
MorphOS, definitely.