Show 1 post and after a specific date show the next one

Assuming, as per the above comment, the format of the dates is YYYY/MM/DD:

$args = array(
    'posts_per_page' => 1,
    'cat' => 6,
    'meta_key' => 'begin_date',        // adjust to actual key
    'meta_value' => date( 'Y/m/d' ),
    'meta_compare' => '>=',
    'order' => 'ASC',
    'orderby' => 'meta_value'
);

$wpse72195_query = new WP_Query( $args );

// do something with the result