Phone crashed, factory reset didn't work, where can I get any old firmware?

[UtherSmith]

Hi, my Samsung SIII GT-i9300 has been randomly switching itself off since I had it.

It recently crashed and I managed to boot it to the recovery menu. I did a factory reset but I still got a long error message saying things like:
E:failed to mount/system (No such file or directory...cant mount/cache/recovery/last_recovery

Now I can't even get it to the recovery menu and the screen is going fuzzy. By holding Power+VolDown+Home I can still get it to the screen that talks about downloading a custom OS.

I have looked up how to do this and have downloaded Odin. The thing I am unable to find is the firmware itself.

Questions
1. Is this a sensible route to take?
2. Where do I find Samsung firmware? Anything will do, it doesn't need to be the latest of anything.

 

[Rukbat]

Instructions are at [Samsung] How to flash Stock ROM via ODIN (if you need them). You should be able to get the firmware from SamMobile Firmwares. (Make sure it's for your model phone, for your country, for your carrier.)

Is it a sensible route to take? It's about the only route to take.