BTW, it *can* have associated custom fields... (your homepage) if you create it as a Page.
Page templates can display one or more categories of posts...it can also have multiple loops. There's nothing different about page.php or index.php... the defaults simply include programming to access the most commonly used elements, like "comments" in your index.php file because comments are associated with posts.
But you can edit either or both or create custom files to use.
For example, make you home content a Page (home) and add the intro text there or use whatever custom fields you need. Then, to get that content, use the standard loop.
To get your category content, add a custom query with categories desired and use another loop, eg:
<?php $my_query = new WP_Query('cat=14&showposts=1'); ?>
<?php while ($my_query->have_posts()) : $my_query->the_post(); ?>
<h2><a href="<?php the_permalink(); ?>"><?php the_title(); ?></a></h2>
<?php the_excerpt(); ?>
<p>Read the rest of "<?php the_title(); ?>" in <?php the_category(' » '); ?></p>
<p class="postmetadata"><?php edit_post_link('Admin Edit', '', ''); ?></p>
<?php endwhile; ?>
The key to this method is
A) the main content loop comes first -- but doesn't not finish the loop with the standard <?php endwhile; endif; ?> --- just the endwhile; statement.
Note that the custom query also uses an endwhile; statement.
B) after you finish all loops, close out with the endif; statement.
C) then point your homepage setting to the static home "Page"
D) the custom query can use more than one category; just list them separated by commas, per the usual and indicate the number of posts to display, etc.