Taking into account your needs, I think that VPS hosting account will be good for running e-commerce web sites.
I know that SolVPS is a good option to order cheap Linux and Windows VPS hosting solutions. Use coupon BESTVPSOFFER for 25% off for life.
Well, smart-web-host.com comes to mind, used them for long time and they are rock solid, quite fast - under 15 minutes response most of the time, you will be pleased.
To my mind with smart-web-host.com you'll get reliable stable cpanel hosting solutions. They are reputable host with trustworthy service and cheap featured plans.
If you are in search of reliable host you should go with Kvchosting.com. You will be pleased with their available support, solid servers and high uptime.
I highly recommend HostingSource as this web host is flexible enough to meet your specific needs.
They have adjusted their pricing plans over time to keep them competitive and currently are extremely competitive in their pricing.
As you're in confusion which one is best for your site. I would recommend Cloud service or VPS for your E-commerce. you can ask them about private Cloud service for your needed.
I would like to recommend you VPS/Cloud instead of shared server because Magento website required higher resources and can cause problem on shared server because of resources restrictions.