I need a shopping cart plugin with customizable checkout form fields

Summary: I am looking for an e-commerce plugin that allows me to add additional fields in the checkout form so I can collect additional data about the customer.

I’m with an elementary school’s PTA and we are selling memberships online via our WordPress site and Paypal. During checkout, I want to get the customer’s billing and payment information, PLUS ask them to identify their student(s) attending our school.

Plugins I’ve tested:

1. WP e-commerce has a customizable checkout form but it is not working correctly in my store (https://bearcreekelementarypta.com/products-page/). WP e-commerce overall seems to be buggy. ??
2. WooCommerce doesn’t seem to have a customizable checkout form.
3. I installed Magento on my server but it is overkill for us (we’re only selling memberships and possible other small items later). Plus I can’t figure out if I can customize the form or not.
4. Paypal itself doesn’t have a customizable checkout form.

I would appreciate any advice. Thanks!