For making any website live, you should have the web hosting service. If you would like to build the small online store then you can host it on shared hosting server. You can use the CMS like WordPress, Joomla, Magento etc. for developing it. Web hosting provider used to provide such CMS for free of cost.
Web hosting service provided the security to your data too.
You will need integration of payment gateway for your online store which can be easily done by web hosting service.