I saw the BTTF movies much later in my life, saw them in 1997 when I was about 16 years old.
The original Part I is the indeed the better movie, perfect screenplay with so many payoffs throughout the film, strong and memorable characters, fantastic musical score, overall great blend of comedy, sci-fi and drama.
But my personal favourite is Part II. After watching BTTF, I became a BTTF fan; but after watching BTTF 2, I became the obsessed BTTF fan.
Watching those Part I scenes from a different perspective in Part II was one of the most unique things I had ever seen, it just blew me away. All the cool 2015 stuff in the first half and the whole adventure of retrieving the Almanac in the second half are some of my favourite scenes from Part II. Also the flying DeLorean became more awesome than it was before.
Part III is equally charming with a new side to Doc's character. We really to get see the growth and chemistry of Doc and Marty flourish in this movie. Also it's a great conclusion to the trilogy, ending on a high note.
And though the first movie can stand on its own, it is more pleasing to consider the BTTF trilogy as a singular story, very few trilogies make you feel that way.