Jose Campos, perhaps better known as the lesser half of the two players the Yankees received for Jesus Montero and Hector Noesi, made only 5 starts in low-A Charleston last year before being shut down with an elbow injury. Luckily, unlike Manny Banuelos, Campos will evidently not need surgery. He's currently throwing off of flat ground, and is expected to be ready for Spring Training.
The "greater" half of that trade, Michael Pineda, didn't throw a single pitch for the Bombers last season after a tear was found in his right/throwing shoulder. He's also throwing on flat ground, but at long distances, and the belief is that he'll be ready sometime around May. Keep in mind that he'll have to be stretched out at that point, so I wouldn't expect Pineda to contribute until at least June.
Finally... Mason Williams. Mason tried to make a diving catch last season, and ended up hyper-extending his non-throwing shoulder. He'd been promoted to high-A Tampa not too long before the injury, and was shut down the rest of the season. Vice President of Baseball Operations, Mark Newman, said that Mason is swinging the bat, which tells me he'll be ready to go by Spring Training.