There are no parameters on the success redirect url but we do have an "On checkout complete" event you can use:
http://helpdesk.smith-consulting.com/...
To enable the event go to your buynow settings "Custom Events" section and enter the url of your web service. You need to create a web service to handle the event and orderID that is passed when the user completes checkout. Then your web service can do anything you like with the order.