C-type asteroid
The largest unequivocally C-type asteroid is 10 Hygiea, although the SMASS classification places the largest asteroid, 1 Ceres, here as well, because that scheme lacks a G-type.
Space colonization
Colonization of asteroids would require space habitats. The asteroid belt has significant overall material available, the largest object being Ceres, although it is thinly distributed as it covers a vast region of space. Unmanned supply craft should be practical with little technological advance, even crossing 500 million kilometers of space. The colonists would have a strong interest in assuring their asteroid did not hit Earth or any other body of significant mass, but would have extreme difficulty in moving an asteroid of any size. The orbits of the Earth and most asteroids are very distant from each other in terms of delta-v and the asteroidal bodies have enormous momentum. Rockets or mass drivers can perhaps be installed on asteroids to direct their path into a safe course.