How to customize commerce order layout
For reference there are a couple answers depending on the situation. The order of the field display can be controlled by going to store->configuration->order settings->Manage Display which I believe would solve the OP question.

If you are looking to setup a custom .tpl.php file I wasn't able to successfully use the template suggestions which are:


commerce_order
commerce_order__commerce_order
commerce_order__commerce_order__customer
commerce_order__OID (where OID is the order ID) 


I found these in template_preprocess_entity in $variables['theme_hook_suggestions']

However, since an order is an entity I was able to use http://drupal.org/node/1238606 (tutorial on theming custom entities) and use a template of my own choosing.

template.php

/**
* Process variables for MYTEMPLATE--order.tpl.php.
*/
function MYTHEME_preprocess_MYTEMPLATE(&amp;$variables) {
  // This is the generic entity preprocessor
  template_preprocess_entity($variables);
}

/**
 * Implements hook_entity_view_alter to alter the entity theme used by
 * commerce_order.
 */
function MYTHEME_entity_view_alter(&amp;$build, $type) {
  if('commerce_order' == $type){
    $build['#theme'] = 'MYTEMPLATE';
  }
}


From there you can use: sites/all/modules/entity/entity.tpl.php as a template for your template.

Hope this helps someone.

Cheers,

Rob