This was another Wordpress issue which proved surprisingly hard to find information on — coding the Wordpress loop for a Page template so that it only displays posts in one post category.
<?php $catID = get_cat_ID( "Category Name" );
query_posts("cat=$catID"); ?>
<?php if (have_posts()) : while (have_posts()) : the_post(); ?>
//Content goes here
<?php endwhile; else: ?>
<p><?php _e('Sorry, no posts matched your criteria.'); ?></p>
<?php endif; ?>
It may be that there’s another way to do this; however this was the way that finally worked for me after a certain amount of wrestling, so I thought I would pass it along. The necessity of the query_posts() tag to retrieve only certain posts is well-documented, and it was easy to find the but less so is the explanation of how one should go about obtaining the parameter for that tag.
The solution to this comes from the get_cat_ID() tag, which retrieves the ID number of the category name which it receives as input. As near as I can tell, this is the only way to find that number, and that number is the only way to get query_posts() to find the posts in the category [ query_posts("cat=#") ].
Hopefully this will help someone who was in the same spot I was in and couldn’t find a solution to how to make this work. If anyone has another way that works better, please let me know in the comments!