Looking for an ecommerce module that remembers customers

I’m trying to convert myself from my old content management system (CMS Made Simple) to WordPress.

So far I have found one big problem I need solving in WordPress. An eCommerce facility that allows users to login, then place an order. A brief summary of the features I am looking for is:

• Ability for the customer to register a username, password, shipping address etc.
• Require email confirmation before allowing the customer to continue
• Allow returning customers to login to their accounts with a username and password
• In the back end interface allow the admin to see which customers have signed up, and have a brief order history.
• Have a destination based shipping system that allows different postage charges.

Personally I did not think that this was much to ask, but so far I have not found a plugin, or set of plugins that does this. I am however rather new to WordPress so am open to suggestions.

Finally, it has to work. Its for a customer who is not that computer literate. I don’t mind setting it up for him, but once setup it needs to be reliable. Endless hard to install updates that break all sorts of things are not acceptable! (see previous CMSMS)