The Giants signed veteran Jameis Winston to a two-year contract last week and have the third pick in next month’s NFL draft.

One draft pick, one contract, one coaching hire—it only takes one wrong decision to send an NFL team spiraling from contender to catastrophe.

While that has plenty of meaning behind the scenes for front offices, fans are most excited for free agency to officially get underway. When the league year begins on Wednesday, March 12, trades that ...