Here's where things get interesting.
If the Giants are in a "win now" mode and believe that last year's 3-13 campaign was a blip on the radar rather than a harbinger of things to come, then there's no need to overthink things — take Saquon Barkley.
Initially it was thought that the Browns would possibly be able take Barkley with the first overall pick and still get their quarterback of choice with the fourth overall pick, but with the Jets moving up to almost certainly pick a quarterback, it's likely the Browns will be forced to take their QB of choice first overall to ensure they get their guy. Should this happen, Barkley would fall right into the Giants' lap.
Taking Barkley would not fill the hole left by Pierre-Paul, nor would it be a step in preparation for the departure of Manning, but it would give New York the most pro-ready player in the NFL Draft. The past two years have shown just how much impact a rookie running back can have on a team — Ezekiel Elliott, Leonard Fournette, Alvin Kamara, and Kareem Hunt have all made the jump and immediately become some of the most feared players in all of football.
If the Giants' top goal is to contend for the Super Bowl in 2018, Barkley would be the obvious choice.