judicious use of a category templates and the query_posts() will help you reach your goal. ah… but you also need to use multiple loops so you can continue to display the normal category:
https://codex.www.ads-software.com/Category_Templates
https://codex.www.ads-software.com/Template_Tags/query_posts
https://codex.www.ads-software.com/The_Loop#Multiple_Loops
create a category.php template, which will be used to display each of your categories. whereever you want to display your headline post place this:
<?php $temp_query = $wp_query; ?>
<?php query_posts('category_name=headline&showposts=1'); ?>
<!-- insert your loop here to display the entry like this simple one below: -->
<?php if (have_posts()) : ?>
<?php while (have_posts()) : the_post(); ?>
<h2><a href="<?php the_permalink() ?>"><?php the_title(); ?></a> </h2>
<?php the_content('Read the rest of this entry »'); ?>
<?php endwhile; else : endif; ?>
// now back to our regularly scheduled programming
<?php $wp_query = $temp_query; ?>
and you can have the rest be the normal loop you were going to use anyway, and it should all display nicely.