THE JOURNEY OF CHIHIRO: this was the first anime movie that I saw and maybe also the first anime in general, I'm not sure. It was so small that I barely remember it but I can remember that the scene where his parents turn into pigs I swallowed, I thought that could happen to my mom and I was scared XD but in general I flipped in colors with the movie since I was used to Western series that treat children as retarded and there was not so there was a plot, complicated characters and even the prota was in danger. that's why I've always liked it so much
There are certainly worse animes to start on ;) But that is nothing compared to the "Hollywood" side of productions O.o
Maid-chan hopes you have watched all the other Gibli animes by now.
And if you want to watch even more anime, Maid-chan is doing reviews of them.