My thoughts here are all speculative since I haven't accomplished this myself or even really attempted to work it out... but!

I've recommended a multi-step solution like this in the past:

1. Require users to create an account if they want to purchase customized business cards. Explain it as they need to do this so their creations can be saved for future purchases.
2. Create a business card node type that uses CCK fields and such to create the business card.
3. Create the business card product that users never actually see. Here's why... you can create a custom form or a cart link that adds this product to the cart with the appropriate attributes/options set to get the price and choices right. When the customer tries to browse to this page, I'd just redirect them to their "portfolio" of business cards... probably most easily accomplished w/ a view listing their business card nodes.
4. When an order is checked out, if I were you I'd create a copy of the customer's "template" node just in case they make changes later. Let them know this, so they don't expect last minute changes to show up in their order. Obviously, the copy you make shouldn't be editable by them, but it wouldn't be a bad idea for them to have viewing access to it somehow to verify they get their order properly.

Those are my thoughts, and it requires you to fill in the blanks in a few places w/ other modules and some custom code. Check out the cart links docs here and in the module settings page itself for more info.