The secret is that the film really doesn't make any sense as a stand-alone -- which is a bit surprising, since the original author of the manga wrote the adaptation. Go read the six-volume manga and it will suddenly all make sense.
Funny you made this thread, as I just watched My Neighbor Totoro and Kiki's Delivery Service for the first time today! I have to say, they were fantastic films. And I watched the dubbed versions. I felt Disney did a great job. I particularly liked the dub of Kiki's delivery service. One difference between the dub version of Kiki's delivery service and the subbed version is that the cat is more sarcastic/witty in the dub. Personally I liked this version better. However, when watching anime, subbed is usually the way to go.
If you're going to watch My Neighbor Totoro, I'd recommend the dubbed version. Elle and Dakota Fanning are terrific as Mei and Satsuki (sisters in the film).