There are literally dozens of elements of an E-commerce website that need to be tested. Many of these things can be tested at one time by running multiple processes at one time. 

When you are working with a software testing company for these purposes, it is important to test small functions as well as the major processes that users will need to successfully and safely complete a purchase.
Explain your concerns completely to the testing company and insist that the initial results of their findings are discussed with you before proceeding with any changes. 

Source: https://www.entrepreneurshipsecret.com/important-things-to-keep-in-mind-when-testing-an-e-commerce-website/