e-commerce plugin

I’m searching for an advice or better solution for an e-commerce site. I’d like to setup a website for on-line ordering. I have a small busines that sels paints for industry and all the products that goes by. Such as thinners, hardeners for paints, sand paper, adhesive tapes and so on. I can prepare hudreds of shades of paints, according to the needs of clients.
I’d like to setup a e-commerce page on which my clients would sign in like on e-bay and then place an order of different products. Like some kind of ordering portal.

Is there a plugin or a theme that operates in such way