Hello!
What is interesting is through their documentation, is you search for the information that is returned in Json. And on your receiving system, do this treatment of Json by feeding a class for example.
Then you map eCommerce information with your bank data!
Your question is a little broad, but advice for your situation would be following the steps below:
1 - Verify and implement a class to access the API
2 - Handle the return information that is in Json
3 - Map your database with the return of the API
4 - The control to save the information you can do by some configuration file or using the Webhooks that the API itself provides!
Here follows the link of the documentation that I use, at first I had to read several times until it became clearer the way it works between my system and Woocommerce http://woocommerce.github.io/woocommerce-rest-api-docs/? php#Introduction
Very wide question... you did not define what is the "integration", what is a "simple product" for you, what is the ERP, what is the database. People have to help in the elaboration of perquntas to be helped.... why many questions here are left unanswered.
– Emanuel Rocha Costa
If you have no idea how to use a REST API imagine how to adapt Woocommerce to your own database.... My suggestion is to search how the wocommerce REST API works and use it, believe me, it’s the easiest way...
– RFL