Custom Blog Loop on Home Page

• don’t use query_posts() for secondary loops – When should you use WP_Query vs query_posts() vs get_posts()?
• get only top level categories
• using 'category__in' should not get posts from child categories

for example:

<?php 
$cats = get_categories('parent=0');
foreach ($cats as $cat) :
  $args = array(
    'posts_per_page' => 1,
    'category__in' => array( $cat->term_id ) );
  $top_cat_query = new WP_Query($args);
  if( $top_cat_query->have_posts() ) while( $top_cat_query->have_posts() ) : 
    $top_cat_query->the_post();
    //output
  endwhile; wp_reset_postdata();
  //..etc..
endforeach;
?>

(not tested)