Each of the e-commerce sites with which we’re familiar have extensive systems for dealing with fraudulent credit-card orders and security issues.
PayPal, for example, offers lots of information in their Help Center. They also have a robust system for managing chargebacks (customers asking for their money back) and unauthorized activities on the account.
The key is to choose a well-known e-commerce platform–they’ll have seen it all and will have good security and fraud-management systems in place. (Picking “Joe’s Shopping Cart System” is probably not a good idea, in other words.)