Custom Checkout

I'm looking to create a website to showcase products and services in a similar style to an online store (offering products, descriptions, prices, etc). I want customers to be able to select the products they desire. These products are stored in a basket (or similar). When a customer has selected all of the products/services that they are interested in they can proceed to "checkout". However, it is at this point where the solution differs from a traditional online store. Instead of checkout and payment i'd like the customers to be presented with a "submit" option, which takes all of the items they've selected, prompts for contact details, and submits these into a queue so i can review and contact the customer to discuss further.

I have been advised that this functionality is not currently a feature within squarespace, however was advised that this forum may be able to advise a way that this could be achieved.

Any help is very much appreciated, and i'm happy to provide more information/clarity if required.

Thanks