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 $variables['theme_hook_suggestions']
However, since an order is an entity I was able to use http://drupal.org/node/1238606 (tutorial on theming custom entities) and use a template of my own choosing.
template.php
/**
* Process variables for MYTEMPLATE--order.tpl.php.
*/
function MYTHEME_preprocess_MYTEMPLATE(&$variables) {
// This is the generic entity preprocessor
template_preprocess_entity($variables);
}
/**
* Implements hook_entity_view_alter to alter the entity theme used by
* commerce_order.
*/
function MYTHEME_entity_view_alter(&$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