Hello,
This can be done with our Variants/Variations features, which can be used to add drop down menus, text entry fields or a combination of both to a product's button:
http://www.e-junkie.com/ej/help.variants.htm
That would allow you to collect the information you need, but you would need to handle the later delivery of the product to the buyer yourself. If it's a tangible product, the features described here will help:
http://www.e-junkie.com/ej/selling-tangible-items.htm
If it is a digital product you will have the buyer's email address and can likely just send them the information that way, since the product will be designed to their specifications there is less risk of them sharing it with others than there is when you are selling copies of the same file to everyone.