I have a IIc. Used to have a IIIc as well but it was a dog (only mine - not a comment on IIIc's generally). Here's a few insights.
The cocking rack. This is a well known point of failure. Once the rack and pinion is worn and a tooth jumps its repair time. Very easy to replace. You can still get racks here
http://www.micro-tools.de/en/Camera-Parts/Kodak/ but they are relatively soft metal, although do work OK.
Lenses. The IIc (& C) has a 2.8 lens, the IIIc has a 2.0 lens. It is said they are the same with just diaphragm restrictions, but I don't know for sure. Forget using different focal length lenses. They are a PITA to use. Just find instructions and read how you have to transfer distance scales. Not worth it. If you want to shoot other than 50mm use a different camera. You can't shut a retina anyway with a different lens on.
Rangefinder. The big Cs have much larger viewfinders than small c's, but otherwise same camera. Only you can say if the extra cost is worth it. They all take great pictures.
Shutters. Seem to be fairly notorious for the usual sticking shutter syndrome. Its a syncro-compur so all usual info applies. You can get into the front fairly easily and a quick and dirty fix is to flush out with solvent and then re-oil gently with tiny amounts of watch oil. It worked on mine and still going strong >2 years later, but a full dismantle and CLA is the ultimate solution. I also have a Retina IIIS and this went on its holidays to Chris Sherlock in NZ a year or two back becaus the string broke. (not a problem on IIc and IIIc). Finally the Reflex lenses do NOT fit the C's or c's, but DO fit the IIIS - which is a non-folder built on a IIIC body - different animal, but a fine rangefinder.
II or III? Same lens sharpness - do you really need 2.0 over 2.8? the III has a meter, but seriously, is a 60 year old meter worth using over sunny 16?
If you see one a good price, its worth getting. Put functionality over appearance and you'll have some fun.