What you are describing can be accomplished with Featured Image and a simple wp_query call.
These are very core elements of a WordPress theme. You’d need to define a size with add image size, and then call it up using the aforementioned post_thumbnail.
Your loop might look something like this:
$args = array(
'post_type' => 'post',
'posts_per_page' => 3
);
$loop = new wp_Query($args);
while($loop->have_posts()) : $loop->the_post();
echo '<a href="'.get_permalink().'">';
echo get_the_post_thumbnail($post->ID, 'my_size');
echo '</a>';
endwhile;
wp_reset_query();