Starting with the halfbacks, Jennings was signed to be the workhorse back and is likely to lead the team in carries if everyone stays healthy. They like him as a between-the-tackles runner and as a receiver out of the backfield, and they will work with him in camp to make sure he can handle the necessary protection responsibilities to play on third downs.
But the wild card is Wilson, the 2012 first-round pick who's coming off neck surgery. Wilson still hasn't been cleared for contact, and while he hopes to receive his clearance July 21, it's no sure thing until it happens. If Wilson can play, he has a chance to become a major factor and challenge Jennings for carries and catches. The Giants believe Wilson offers a home-run threat from the running back position, and if he's healthy they will find a way to get that into their lineup.
Hillis, the veteran, impressed the Giants in a short trial last year as a pass-blocker and a receiver. But at this point in his career, he's a backup who could be beaten out for his roster spot. Williams, the rookie, is a fourth-round pick who led the NCAA in rushing yardage last year at Boston College. He's a work in progress but will get a chance to develop in the new offense as a between-tackles runner. Cox, the 2013 seventh-round pick, was able to stick last year because the Giants needed him on kick returns. This year, he'll have to make the team as a running back, and a healthy Wilson could make that tough. Same with Gaskins, who got a lot of looks in minicamp with Wilson sidelined but is a guy the coaching staff likes.
*As for fullback, this shapes up as a straight one-on-one competition between Hynoski and Connor, who signed last year when Hynoski got hurt. Tough to handicap it at this point, but if he is healthy Hynoski could have the edge as a player the Giants know better and who's shown an ability to contribute something as a receiver out of the backfield. They like them both as blockers, but Hynoski is a bit better on the rare occasions when the fullback has to have the ball in his hands.