Part I is certainly the cleverest of the three. A rip-snorter of a premise: Marty (Michael J. Fox) is accidentally sent back to 1955 in the time machine that his friend Doc Emmett Brown (Christopher Lloyd, in a zany, unforgettable, over-the-top performance that creates one of the best characters of all time) has built, and he accidentally interferes in the meeting of his parents, so that instead of his grandpa hitting his father (Crispin Glover in another over-the-top but crucial and memorable performance) with his car, he hits Marty instead. So instead of Marty's mother falling in love with his father, she falls in love with him! Controversial and awkward though it may be, you can't deny its greatness. The real aim of this, though, is not incest, its learning what his mother was really like in her youth, compared to how she tells it. Plus, it lends a certain urgency to what Marty must do to set back the course of time, which makes us need to watch till the end to see he does it: he must somehow make his parents meet and fall in love, or he won't be born!
The second main quest in the movie is the technical problem of getting Marty back to the future: since in Part I the time machine runs on plutonium, and plutonium doesn't exist in 1955, they have to find some other way of generating the 1.21 gigawatts needed to get the car to 88 miles per hour and send it into time.
The third main problem of the movie is that on the day when Marty got sent back in time, in 1985, Doc will be shot by Libyan terrorists for stealing their plutonium to run the time machine, unless Marty does something about it. A terrific feature of these movies are their climaxes: Part I is a terrific scene where Marty must hit the power line connected to the clock tower at 88 miles per hour at the precise moment lightening strikes it, involving a reference to a famous silent movie image, of Harold Lloyd hanging from a clock high on a building in Safety Last (1921).
Back to the Future pulls a lot of old punches, uses a lot of traditional storytelling gags and devices that feel quite familiar, but its unabashed sense of fun, larger-than-life tone and ripsnorter premise make it the kind of movie you treasure and watch time and time again.