Need eCommerce with special abilities

Hello all,
I am currently working on a project for a grocery delivery business.

They would like a website in which visitors can register and place their orders for groceries online. The order form would consist of something similar to workingmom(dot)com/grocery_list/ where they check what they want to be purchased. Once they submit the form, it effectively orders it, sending an email with the order to the business owners. It is also preferable that their is a backend where they can manage customers and orders.

Furthermore, the order should be saved in an order history for each customer. Each customer should be able to go back, view a past order, and then modify that previous order and submit it as a new order.

It is fairly different from most eCommerce so I don't expect their to be something like this out of the box. What would be a good basic eCommerce script that I could begin with to eventually achieve this?

What programming language?

Preferably PHP

You may want to try X-Cart. It's admin UI is pretty poor, but it's not difficult to modify at all. The code design isn't awesome either, but it's OK. It covers pretty much everything you need except your custom order form and the re-ordering thing.

PrestaShop is another E-Commerce system that I've seen more of recently, although I have never actually used it myself so I do not know how easy it is to modify. The admin UI seems like a step up from X-Cart.

I would stay far away from osCommerce, as it's code is pretty much downright terrible, and Zen Cart falls into a similar category although it's not as bad.

Magento has pretty extensive features, probably more than you need, but it has poor performance and is a PITA to modify.

Do you know the marketplace solution? it's a one-stop shop solution with different merchants. Orders will be automatically transfered to the merchants. The back office of the platform is very easy to use among customers, merchants and owners of the solution. It is a highly customized solution. You can search The MP Factory website for more details.