How to get to know a Customer's Journey?

Given the case I have an online-shop and use some advertising channels to generate traffic, which converts now and then. Now I would like to create a report, showing me all users (customer) who made an order (reached specific goals). Later on, I would like to see every customer’s journey (“path to conversion”), i.e. all advertisments the customer had contact with. This allows me better evaluate the performance of my various advertising channels.

Is there already a way to achieve this? What would be the best approach to achieve this?

I do not necessarily need you to implement this. I only require some guidance on how to do this the most appropriate way.