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.
+1 on Chris Sherlock, he CLAd my IIc and it is like new.
The IIc has a smaller, dimmer viewfinder than the IIIC, but it is still a superb camera, small, great built, superb lens (mine has the Rodenstock, but the Schneider should be similar). I love it as a travel camera.
The buttom wind lever is convinient, the EV setting is, to me, the most intuitive way to do it.
Thanks guys, very informative.
Finder on IIIC (large C) is much better if you wear glasses.
The IIIC was my first 35mm, my aunts gave it to me for high school graduation in 1966. Still have mine, meter still works, optics were very good for the time. After moving to SLR the next year I found that the swithing from a Pentex and Konica T to the III took a little getting us, film winder on the bottom, setting the expousre using the interlocking EV scale takes a moment to remember what to and the steps, same for rewinding and loading film. The viewfinder is good. I have both the 35mm and 85 lens, but have not used them in decades, just a wast time, very slow and heavy. What I do like about the IIIC, other than an emotional attachment, is that it folds up and fits in my 4X5 bag. If you want a folder the IIIC is ok, but if just want an odd rangfinder look at at the IIIS.