With paypal IPN, paypal will automatically run a specified script once payment is made. In this script you can add info into your database, such as which user made the payment, txnid(transaction ID), payment amount, payment status. All things that may be useful in the future. Here are some useful links:
IPN documentation.
IPN setup walkthrough
You will need to activate IPN in your paypal settings and input a script for paypal to run.
You can also setup this script to "render the appropriate service to that customer" as you mentioned above.
Once you have ipn and database insertion up and working you could add a php mail function to the script to inform yourself of which user has made a purchase:
<?PHP
//mail variables
$emailAddress = "your@email.net";
$subject = "User Purchase";
$message = "$user has made a purchase of $product for $productPrice";
$headers = "MIME-Version: 1.0" . "\r\n";
$headers.= "Content-type:text/html;charset=iso-8859-1" . "\r\n";
$headers.= 'From: noreply@yourdomain.com' . "\r\n" .
'Reply-To: noreply@yourdomain.com' . "\r\n" .
'X-Mailer: PHP/' . phpversion();
//mail function
mail($emailAddress, $subject, $message, $headers);
?>
This mail function can also be used for debugging purposes. Just add information/variables you need to debug into the $message variable and you will receive an email everytime the script runs.