For listing products, you can use e.g. the ListPage or AppListView components.
For a shopping cart, the Storage item can be used to store user data (e.g. the selected products) locally on the device.
This is comparable to what we did for the Qt World Summit demo app, which allows saving favorites.
With a WebStorage you can even store data in the cloud and sync it across devices if the user is logged in with Facebook.
Another option for user authentication and cloud storage would be the Firebase Plugin.