I would highly prefer isolated environment such as VPS Hosting to host ecommerce websites. Because ecommerce websites are heavy and resource hungry compared to an average website and it demands dedicated resources.
Ordinary shared hosting environment cannot handle load of these websites. Though you want to host your store in shared host, I could suggest you AccuWebHosting.com as the excellent Web Hosting provider with highly optimized web server specially for the PHP based CMS such as WordPress, Magento, Joomla, Drupal etc. Instead of conventional LAMP environment, AccuWebHosting offers Highly optimized Web Hosting environment for PHP based CMS which includes:
CloudLinux as OS :: Reputable, Secure, and High Speed OS
LiteSpeed as Web Server :: #1 Commercial Web Server - 7x Faster
100 % SSD Drives :: Pure SSD Storage Means Insanely Fast Websites
You will get FREE IP address on purchase of SSL certificate. I am not sure with the web hosting performance of web host you mentioned. However, you can google for the same and check their reviews at trusted website and forums.