Harry,
I have pointed this out to many users of WordPress that the framework in inherently slow.
WordPress is a good framework but it was designed as a one size fits all framework for blogging. What does that mean to you as a developer? There are many areas of the WordPress framework that many people do not use but still must be loaded in order for the framework to work. That is just the nature of the beast. Whenever you use a framework you have to take the pros and the cons that come with the framework.
When you start adding additional features to WordPress in the form of plugins, you actually make the situation worse. These plugins add additional features to WordPress framework that were not a part of the original development or core code and modify the original code to support the plugin. Many of these features are not optimized with the core functionality of the framework in mind and some even conflict with the core code development. This can open security holes in the core development. These plugins also add features that you probably do not use but must be there in order for the plugin to work. The more you add the more bloat that becomes part of the WordPress core code.
There are even plugins that are supposed to speed up the operation of WordPress, and in some aspects they do, but again they also add additional code to the core code. Which can open security issues and impact speed of the operations of some of the features you may be using.
When moving into eCommerce your biggest concern should be security and there are some major issues with security features in WordPress. Google it, you will find hundreds of articles and white papers on the security concerns with WordPress. Because of the popularity of the framework it is a big target for hackers. The more popular a framework the more visibility the framework will get, the bigger the target it becomes.
On eCommerce sites, it is best if the site is written from scratch for the that particular site. Controlling all the code that is involved with a customer transaction and keeping the core code to a minimum keeps the site running efficiently and keeps its secure. Probably not what you want to hear, but it is the truth.
You can try some of the speed plugins for WordPress, but as stated many of them actually add bloat to the code and may slightly increase speed, but at what cost, if they add security issues or holes in the code are you willing to take that risk with your customer data.