Have latest post and recent posts display differently

You need 2 queries e.g.

$query1 = new WP_Query( 'post_type=post&posts_per_page=1' );

// The Loop
while ( $query1->have_posts() ) {
    $query1->the_post();
    echo '<li>' . get_the_title() . '</li>';
}
wp_reset_postdata();

$query2 = new WP_Query( 'post_type=post&posts_per_page=100&offset=1' );

while( $query2->have_posts() ) {
    $query2->next_post();
    echo '<li>' . get_the_title( $query2->post->ID ) . '</li>';
}

wp_reset_postdata();

The first query gets the first post (which you can then do what you want) and the second query gets the rest of the posts but skips the first post (from the first query) using the offset tag.