Thank you for your response, E-junkieNinja.
However, I'm still a little confused if the options described in the link you posted will allow me to successfully integrate the E-Junkie shopping cart into my website.
Basically, when a customer visits my website to make a purchase s/he is asked to supply information for several fields prior to clicking the "Add to Cart" button. These fields include whether s/he would like to order a "Dozen/Half-Dozen" [muffins], whether they'd like to have the muffins "Shipped/delivered/pick-up", and (if they select "Deliver/Pick-up") a date for when they'd like to have their item delivered/picked-up. These values need to be passed to the shopping cart, mostly so that I can see them to know how to respond to a customer's purchase.
Based on your opinion with the E-Junkie shopping cart, will it be up to the task given the information I have provided you?