256MB is not so low on Panther. Minimum was 128MB back then, but 512MB+ is still recommended. As for Kernel panics, it could be low RAM, bad RAM, a software issue, or some other hardware problem. TCP is spot on about a G4 board and CPU. I suppose you might get a G5 from an iMac, but you would need most of the rest of it too. A PowerMac G5 is out of the question, and probably too pricey at the moment. They are all falling out of warranty at the moment so the market for spares at non-Apple prices is going to be fairly strong for a while. Which means parts will be just below Apple price.

Just get as much RAM as you can for whatever you end up with, and a bigger HD might make the thing alot more useful. Depends what you want to do with it really.