Should your story have quotes at the beginning of each chapter or should each chapter have its own title instead?

you could use either, but i think it is interesting reading a book that has quotes at the beginnings of chapters that give you a clue of what is going to happen in that particular one, because when you have read it you can understand and appreciate the quote and why it was chosen. It would, however, if you are thinking of writing a book with lots of chapters, be quite hard to think of all of the different quotes for each chapter, whereas with titles it is much easier to think of something that summarises or makes the reader want to read on.