One post on frontpage and an archive page

Alter the main query for the front/home page with is_front_page() and/or is_home(), like shown below:

add_action('pre_get_posts','wpse104878_alter_main_query');
function wpse104878_alter_main_query($query){

    if ( is_admin() || ! $query->is_main_query() ) {
        return;
    }

    if( $query->is_main_query() && is_front_page() || is_home() ){

        $query->query_vars['posts_per_page'] = '1';

    }

}

The archive page should work, if underscore starter theme has an template for it. You can alter that separatly – similar to above function – with is_archive().