How to link to category and list post under category

Can someone help me with the code below, I’m a designer and not too familiar with php.

<ul>
				<?php
				// get all the categories from the database
				$cats = get_categories(); 

                // loop through the categries
                foreach ($cats as $cat) {
                    // setup the category ID
                    $cat_id = $cat->term_id;
                    // Make a header for the cateogry
                    echo "<li>".$cat->name."</li>";
                    // create a custom wordpress query
                    query_posts("cat=$cat_id&post_per_page=10");
                    // start the wordpress loop!
                    if (have_posts()) : while (have_posts()) : the_post(); ?>
                        <?php // create our link now that the post is setup ?>
                        <li><a href="<?php the_permalink();?>"><?php the_title(); ?></a></li>
                    <?php endwhile; endif; // done our wordpress loop. Will start again for each category ?>
                <?php } // done the foreach statement ?>
			</ul>

I actually want it to print…
– Link to category
– Instead of post title, just increments of 1,2,3.
– post nested within category.

How can I get it to print like the below….

<ul>
	<li><a href="">category name</a>
             <ul>
                  <li><a href="/">1</a></li>
                  <li><a href="/">2</a></li>
                  <li><a href="/">3</a></li>
             </ul>
        </li>
	<li><a href="">category name 2</a>
             <ul>
                  <li><a href="/">1</a></li>
                  <li><a href="/">2</a></li>
                  <li><a href="/">3</a></li>
             </ul>
        </li>
</ul>