I was raised by geek parents, so I ended up seeing most of the classic movie staples (at least, in the sci-fi and fantasy genres) at a young age. I also loved Disney, but Mulan was the only princess movie (Lilo and Stitch remains my favorite Disney movie).
Also, the new Star Wars is THE BEST THING but the others are kinda meh in comparison, and you could totally just read the plot synopsis for episodes 4-6 on Wikipedia and then watch the new one. 
I'd have to disagree with you there. The new movie was indeed awesome, but part of what makes it awesome (at least, for me) was the way it harkened back to the original trilogy, thematically and with little in-jokes and such. A synopsis of those movies would certainly get you caught up enough to enjoy the plot of the new one, but you'd probably miss all that awesome little stuff. (I'm a fan of the original trilogy for itself, anyway, but I respect your opinion

)
Also, Monty Python is the best and also hilarious. I didn't watch the Princess Bride until last year, but it was likewise awesome!
Sidenote for Back to the Future: at this point, even the "future" parts of the movie take place in the past
