Like a sketch: Prestashop or Magento would be reasonable solutions for the start-up businesses. They both have responsible templates for desktop, tablets and smart phones. Your web eCommerce start up web site would look great that way.
You have the option to create dedicated mobile site for your eCommerce, but this is horrible if you don’t like to manage basically two different web sits: one for desktops and other for mobile. Though, in terms of performance may be smart solution if you are one of the “big guys”.
You can create Android app for your eCommerce start up, and make it available on Google play app store. Same for the iPhone app store.
What would be the anatomy of the online store?
You would need to set the products and categories catalog in your webstore. Product search is a must, but almost all the eCommerce systems support that. For your eCommerce, you define the shipping methods and payment methods if you don’t sell downloadable products.
Your customers would probable need the accounts, so they can log in and access specific areas of your web site. They would probable need multi currency payment option on your eCommerce web site – but not critical.
If you create the start up website, your webmaster, would need to have all possible reporting and analytic reviews to balance your income. This way you would know what part of the world your customer came.
You would probable need cool features called “latest products” and “popular products”. You can put these info to the landing page.