Images Pulled from Category-Specific Posts

I’ve spent a good part of the last few days researching how to accomplish this task. I know there is a lot of information out there about how to do this, but for some reason they either don’t work for me specifically or I have a hard time wrapping my brain around it. I hope someone here can help, and I apologize if this has already been answered elsewhere.

My goal:
I am creating a portfolio for myself through WordPress that acts, or at least looks, more like a website than a blog. My Index page has sections for Recent Projects (under the category “Portfolio”) and Latest News pulled from my blog (category “Design”) and Latest Freebies (category “Freebies”).

Here is what I have so far: variaga.com

I was able to get the last two sections working how I want them (I have yet to format any other pages other than the Index) but am having trouble with the Recent Projects section.

In that section I would like to show only 6 thumbnails of the most recent posts in the “Portfolio” category in the given space that, once clicked on, will take you to the page that contains the project/post in full.

Here’s what I have for the Index.php page:

<?php get_header(); ?>
	<div id="content">
    	<div id="recent">
        	<div id="recent-head">
        		<h1>Recent&nbsp;Projects</h1>
            	</div>
            	<div id="recent-content">
			<ul class="recent-projects">
            			<li>
                		<a href="#"><img src="images/sample.jpg" /></a>
            			</li>
            		</ul>
            	</div>
        </div>
        <div id="3col">
        	<div id="about-head">
        		<h1>About&nbsp;Me
			</h1>
            			<div id="about-content">
					<div id="me">
					</div>
					<br />
                    			<p>
                        		Victoria Arriaga<br />
                        		Sacramento, CA<br />
                        		Artist &brvbar; Designer
                    			</p>
                    			<p class="clear">Interests: Web Design, Print Design, Typography, Science Fiction, Linguistics, Music, Travel, Photography
                        		</p>
            			</div>
            	</div>
            	<div id="latest-head">
        		<h1>Latest&nbsp;News</h1>
         			<div id="latest-content">
                    		<?php query_posts("category_name=design&showposts=5"); ?>
					<ul class="recent-posts">
        				<?php while (have_posts()) : the_post(); ?>
						<li><a href="<?php the_permalink() ?>" rel="bookmark" title="<?php _e('Permanent link to'); ?> <?php the_title(); ?>"><?php the_title(); ?></a>
            				<br />
						<span class="post-month"><small><?php the_time('m-d-Y') ?></small></span>
            					</li>
        				<?php endwhile;?>
                        		</ul>
           			</div>
            	</div>
            	<div id="freebies-head">
        		<h1>Latest&nbsp;Freebies</h1>
            			<div id="freebies-content">
                		<?php query_posts("category_name=freebies&showposts=5"); ?>
					<ul class="recent-posts">
        				<?php while (have_posts()) : the_post(); ?>
						<li><a href="<?php the_permalink() ?>" rel="bookmark" title="<?php _e('Permanent link to'); ?> <?php the_title(); ?>"><?php the_title(); ?></a>
            					<br />
						<span class="post-month"><small><?php the_time('m-d-Y') ?></small></span>
            					</li>
        				<?php endwhile;?>
                       			</ul>
           			</div>
		</div>
        </div>
  	</div>
    <!--/content-->

</div>
<?php get_footer(); ?>
	<!--/footer -->
</div>
<!--/page-->
</div>
	<!--/wrapper-->

</body>
</html>

I hope I made some sense. :]