Part I is the more digestible version (and the Urfaust even more so). Heinrich Faust, a scholar who is trying to reconcile the life of the mind with the lusts of the flesh, signs a deal with Mephistopheles (who9 first appears, and I am not making this up, in the shape of a poodle) to get whatever he wants, notably the pretty girl Gretchen. There are various rustic and studenty comic interludes, but it all goes wrong and she is executed for infanticide (I think; it's a bit obscure).
Part II, in five tedious acts, is more a pageant of Goethe's knowledge (and adaptation) of German and classical mythology than anything resembling an actual plot. Faust sets up a kingdom which seems to be co-located between medieval Germany and ancient Greece in order to seduce Helen of Troy (after the end of the Trojan war). There are complicated bits with emperors battling each other (one of whom may be Napoleon, who was around at the time of composition) and I really didn't follow much of it.
I think that either part would be pretty much impossible to stage. The characters do very little but wander up and down declaiming verse, and some of the directions are surely unimplementable (the well-trained poodle, as noted above; various stunts required in Part II). I assume that Goethe wrote it for intellectual house parties to recite to each other while lounging around the formal gardens sipping white wine.
Despite the fact that I really didn't enjoy Faust much, I did have some fun spotting themes that have carried through to later literature. Quite a lot of Part I reminded me of Buffy, with the students, young lurve, supernatural powers and diabolical figures tempting our lead character. That may be my imagination; I'm quite sure, however, that Roger Zelazny drew on Faust's construction of his magical castle to seduce Helen when writing the latter part of Jack of Shadows - he was a fan of German literature.
I suppose I should read (or, better, somehow watch) the Marlowe version to get another perspective on the story. (And then reread Michael Swanwick's take on it.)