Input on what plugins to use

I am going to make a site that will have ‘product pages’ that can be added to a cart with a downloadable zip file.

I want the site to be partially accessible to public but mostly accessible through managed accounts.

So when logged in to your account, I would hope you could visit a product page, add the product to your list / cart, and then be able to see your profile / cart at which point you can download the package.

Any input on what plugins could make this happen would be appreciated.

No transactions will need to be completed on this site, i just simply need a form of User Page that can maintain a list of preferred downloads.