The limiting factor is likely to be with clearances in your frame, fork, and brake calipers rather than just the rim width. I've found that you can go well beyond the recommendations at Sheldon's site without having problems with a tire that's wider than shown for a given rim size. Check how much clearance you have with your current tires at the point where they come closest to touching something and that should give you a good idea of how much wider you can go.
As to the 'C', it should be associated with the 700 rather than with the 25 - so the size should be 700C x 25 (but is frequently mislabeled). At one time there were a series of different wheel sizes that all ended up with the outer diameter of the tire being about 700mm. They had different widths and the rims intended for use with narrowest width tire had the largest diameter and were designated 700A. Rims for wider tires (and therefore slightly smaller rim diameters) were labeled 700B, 700C, 700D. Eventually all but the 700C size rim were dropped and rims with that diameter (actual measurement of 622 mm) are now used for a wide variety of tire widths.