I liked FFVIII's beginning as a whole, but my favorite scene from a beginning would have to be when they are all sitting around the fire at the start of FFX. It was so sad, and it made you want to get to know who all those people were.
As far as endings, I am going to have to hold out until I finish XII. If I had to choose now, I would prolly go with X-2, especially the Good ending (SPOILER)when Yuna runs out of the airship and hugs/tackles Tidus. What can I say, I like happy endings.