Cart that allows collection of customer entered data

I’m new to WordPress but I’m really enjoying it. I am after some advice for a website I am helping a family member with.

They run a company that provides a family history research service and we would like a simple cart system ie. we don’t need products, downloads, shipping, variations. All we need is to be able to define 10 or so fields (dropdowns, radio, text fields) for the information the customer wants researched. The page just needs to allow customers to enter their order in the fields, click add to cart, and check out at the end. So far I have only found plugins that support variations but none that seem flexible enough or that I can understand anyway.

Does anyone have any suggestions?

Thanks in advance,
PB.