Jack and the Beanstalk has the honour of being the only one of the four fairy tales used with roots in English. It, like the others, had been told orally for an eternity before somebody actually got around to writing it down. That somebody was Benjamin Tabart in 1807. Tabart's story was based on folklore, but he introduced his own context by having Jack bump into a fairy when he climbs the beanstalk. The fairy tells him the giant killed his father and stole his stuff, thus giving Jack justification for taking it. This justification was false, and luckily removed in later versions.
In 1860, the Australian folklorist Joseph Jacobs felt it his patriotic duty to recapture the English fairy tale (back then Australians felt British, some still do). He removed the fairy, and trusted children to see that Jack was not necessarily in the right. This trust of course has paid off, in that the entire second act of Into the Woods rests on the consequences of Jack's actions, and it is important you can see the side of the giants, even if you want them to lose.
While Jacobs's version of the story did not originate any concepts, it is perhaps the best indication these days of what was present in the original story. It does include the name Milky-White, and the gold, the hen and the harp, though the list of items does change between versions.
An important thing to note in Jacobs's version is that the giant's wife is kind and welcoming on Jack's first visit, but later sides with her husband when she discovers Jack stole from them. The elements added to the story centre around Jack's motives for returning. In Jacobs's version it is purely greed (as Cinderella accuses him), but in Into the Woods he has the extra motivations of Little Red's taunting, and also getting Milky-White back, which he never cared about in original versions.