You appear to want to save the lowest cost of each shipping module to your order ...

For USPS you could customize the code:
/includes/modules/shipping/usps.php

around line 380 to include the code in RED:
Code:
      // bof: save lowest cost to $_SESSION['shipping_rate_usps']
      $_SESSION['shipping_rate_usps'] == 0;
      // eof: save lowest cost to $_SESSION['shipping_rate_usps']

      for ($i=0; $i<$PackageSize; $i++) {
Then around line 566 include the code in RED:
Code:
        $cost += (MODULE_SHIPPING_USPS_HANDLING_METHOD == 'Box') ? $usps_handling_fee * $shipping_num_boxes : $usps_handling_fee;
        // bof: save lowest cost to $_SESSION['shipping_rate_usps']
        if ($_SESSION['shipping_rate_usps'] == 0 || $_SESSION['shipping_rate_usps'] > $cost) {
          $_SESSION['shipping_rate_usps'] = $cost;
        }
        // eof: save lowest cost to $_SESSION['shipping_rate_usps']
        // set the output title display name back to correct format
        $title = str_replace(array('RM', 'TM', '**'), array('&reg;', '&trade;', ''), $type_rebuilt);
Maybe this will help you on the other shipping modules ...

NOTE: I have not tested this code