A Page that shows posts from a category?

Don’t use a page for this, just use the category archive with a category description (Dashboard -> Manage -> Categories). Make sure that your category template shows a category description.

https://codex.www.ads-software.com/Category_Templates
https://codex.www.ads-software.com/Template_Tags/category_description

For showing all posts, use a plugin or query_posts in a category template.

https://codex.www.ads-software.com/Template_Tags/query_posts

I list all of my post titles in my category archives using this:

<ul>
<?php $posts = query_posts($query_string . '&orderby=title&order=asc&posts_per_page=-1'); while (have_posts()) : the_post(); ?>
<li><a href="<?php the_permalink(); ?>" rel="bookmark"><?php the_title(); ?></a></li>
<?php endwhile; ?>
</ul>