The important thing you need to test is the performance of your ecommerce website/application. You need to conduct performance testing on parameters such as webpage loading speed, throughput, data transfer rate, efficiency, uptime, database performance, website traffic load tolerance, error messages, etc.
You need to make your ecommerce website is having high search engine visibility so that you can get considerable user traffic to your site. You can do this by implement search engine optimization (SEO) on your website. You need to test whether SEO strategies such as title tags, meta-descriptions, URL structure, image alt tags, etc are implemented correctly.