I've done this with PHP. I've worked with ASP before, it's not that different, so I may be able to do the solution in ASP as well.
Have you looked at Braintree? The problem with your typical CC solution is that the card goes across your server, meaning YOUR server has to be PCI compliant (not easy) and you are on the hook for any loses your customers incur if your server gets hacked. Braintree provides a javascript intermediary solution which sends the CC info directly to their server from the browser (via javascript), and returns a special token that your script then sends to the server to use on the backend for processing the payment. They are owned now by paypal and have super easy paypal integration for this.
Anyway, would love to chat and discuss if you like.
Regards,
Joseph Cardwell