Looking for advice for a mail sending plugin

There is no need for a custom table here – you can use the user metadata table and API.

Then create a WP-Cron job to run every 24 hours (or more frequently if you’re paranoid). On the callback query users who’ve registered in the last 7 days using something like:

/*
 * Get all users registered after $start and before $end (dates in yyyy-mm-dd format)
 * Based on my answer to this question: http://wordpress.stackexchange.com/questions/51485/how-can-i-query-all-users-who-registered-today/51492#51492
 * @param (string) $start - start date in yyyy-mm-dd format
 * @param (string) $end - end date in yyyy-mm-dd format
 */
function wpse51485_get_users_registered($start="", $end='' ){
    global $wpdb;

    if( empty($start) )
        $date = date('Y-m-d');

    if ( empty($end) )
        $end = $start;

    //Should probably validate input and throw up error. In any case, the following ensures the query is safe.

    $start_dt = new DateTime($start. ' 00:00:00');
    $s = $start_dt->format('Y-m-d H:i:s');

    $end_dt = new DateTime($end.' 23:59:59');
    $e = $end_dt->format('Y-m-d H:i:s');

    $sql = $wpdb->prepare("SELECT wp_users.* FROM wp_users WHERE 1=1 AND CAST(user_registered AS DATE) BETWEEN %s AND %s ORDER BY user_login ASC",$s,$e);

    $users = $wpdb->get_results($sql);

    return $users;
 }

and finally loop through them, and send an email if required (using and updating the user’s meta appropriately).

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