It's really all going to depend on the rules of your credit card, and how it's allowed to be given funds by the company that issues it. By the sounds of your needs, it would probably be easiest to create a Paypal account, verify your paypal account by meeting their fairly simple verifying criteria, and then ask them to send you a free debit card for your account in the mail. Then you can use paypal to collect funds by using paypal buttons, the social store, and etc.
Linking a credit card to your website will have to have some sort of third party action as described above.
