Hi,
Then, I suppose that there is one main thing you need: loading and updating the products data from the website to the app.
One thing you could do would be to configure the Google products plugin to generate a XML of the data of the products and then have the app retrieve that XML and process it, once in a while.
For the payment, the best would be to go through the payment capabilities of Google Play and Apple's app store. That way, it will be a lot more seamless for the user than going through your website inside the app.