post preview/thumbnails not displaying correctly- linking to “home” instead of post?

It sounds like you need a second loop on your home page to call the 3 most recent posts. Try something like this:

// Main home page content here

<?php $my_query = new WP_Query( array( 'posts_per_page' => 3, 'nopaging' => true ) );
while ( $my_query->have_posts() ) : ( $my_query->the_post() ); ?>
<div id="preview">
    <div id="preview-item">
        <div id="preview-headline">
        <a href="https://wordpress.stackexchange.com/questions/52846/<?php the_permalink(); ?>"><?php the_title(); ?>
    </div><!-- end preview-headline -->
    <div id="preview-thumbnail">
        <?php the_post_thumbnail( array(120,102) ); ?> 
    </div><!-- end preview-thumbnail -->
    </div><!-- end preview-item --> 
</div><!-- end preview-->
<?php endwhile; ?>

// Closing Home page content here