There is a way, you would have to do a little work in your theme to add a function to the loop to look for a set group of posts with certain categories first and then fill in the rest.
(For the important posts. Category #5 is set for top priority)
<?php query_posts('&cat=5); ?> <!-- Edit the cat= part to the number of the desired category (check the category IDs in your WordPress system), and this will show the 1st of the chosen category -->
<?php while (have_posts()) : the_post(); ?>
(Then let the rest of the posts come in. Make sure the category in this string is set to -5 to prevent duplication)
<?php query_posts('&cat=-5'); ?> <!-- Edit the cat= part to the number of the desired category (check the category IDs in your WordPress system), and this will show the 1st of the chosen category -->
<?php while (have_posts()) : the_post(); ?>