You can use <h1> for each story, and <h2> for the chapters. Some people like using <h1> for the book title instead, but I find it unnecessary (I don't include the book title as an item in the TOC, anyway). But you could also use <h2> and <h3>, or <h5> and <h6>...
<div> are for marking generic blocks. They don't have any default styling, so any formatting you want to apply to them must be done with CSS, and for every different kind, you use a different class. Which ones to use depends on your book. The separations using "* * *" are a good candidate for a <div>:
Code:
<div class="scene_break">* * *</div>
and then with CSS you make it centered, and with some top and bottom margins. I often use <div>s for centered blocks, signatures, poetry...
As for other tags, I guess the main one is <blockquote>, which you can use if there are letters or quoted fragments in your books. And there's inline tags, such as <i>, <b>, or the generic <span>.