If you would like to have online store, go with Shopify.
For blog, go with Wordpress.
I ever tried Wordpress for online store and it is working fine, but lack of function of e-commerce.
At the end, you will need to install so many plugins to have complete online store solutions on Wordpress.
With hosted service like Shopify, all is there.
If you need to tweak by your own, you can try OSCommerce, Prestashop, etc.