If you want to check if the customer is a guest, registered or just register to the site when they place the order, below script will help you identify that in success.phtml file.

You can find success/order confirmation phtml file at:
app/design/frontend/[package]/[theme]/template/checkout/success.phtml

Just at the end of this file put below lines of code:

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<?php $order = Mage::getModel('sales/order')->loadByIncrementId($this->getOrderId());
$quoteId = $order->getQuoteId();
$quote = Mage::getModel('sales/quote')->load($quoteId);
$method = $quote->getCheckoutMethod(true);
$customer_email = $order->getCustomerEmail();
if ($method == 'register'){ ?>
//code to handle if customer just registered to your site
<?php } elseif($method == 'guest') {?>
//code to handle if customer is guest
<?php } else { ?>
//code to handle for logged in customer
<?php } ?>

In the same file, success.phtml, you can request for order number, customer email, customer id, subtotal, grandtotal, order ID just created etc. like this:

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$_customerId = Mage::getSingleton('customer/session')->getCustomerId();
$lastOrderId = Mage::getSingleton('checkout/session')->getLastOrderId();
$order = Mage::getSingleton('sales/order');
$order->load($lastOrderId);
$_totalData =$order->getData();
$_sub = $_totalData['subtotal'];
$_orderEmail = $_totalData['customer_email'];
$_orderNumber = $_totalData['increment_id'];