First there is excerpt avaIlable in the page posts. Just set it in the Screen Options.
About the code try this one which I use on my projects.
It will show excerpt of those pages, which have custom field named showOnHomePage and the value of this field determines the order in the list.
$pages=get_posts( array( 'meta_key' => 'showOnHomePage', 'post_type' => 'page', 'orderby' => 'meta_value', 'order' => 'ASC'));
foreach( $pages as $page )
{
echo '<h2 class="entry-title"><a href="'.get_permalink( $page->ID ).'" >'.get_the_title( $page->ID ).'</a></h2>';
echo $page->post_excerpt;
echo '<a class="read-more" href="'. get_permalink( $page->ID ) . '">Read More</a>';
}