You should take a look at content.php and do a check for is_post_type_archive() on whatever you want to hide. For example to hide the entry-meta section, you can do the following:
<?php if ( !is_post_type_archive() ) { ?>
<div class="entry-meta">
<?php
if ( 'post' == get_post_type() )
twentyfourteen_posted_on();
if ( ! post_password_required() && ( comments_open() || get_comments_number() ) ) :
?>
<span class="comments-link"><?php comments_popup_link( __( 'Leave a comment', 'twentyfourteen' ), __( '1 Comment', 'twentyfourteen' ), __( '% Comments', 'twentyfourteen' ) ); ?></span>
<?php
endif;
edit_post_link( __( 'Edit', 'twentyfourteen' ), '<span class="edit-link">', '</span>' );
?>
</div><!-- .entry-meta -->
<?php } ?>