Most shopping cart solutions offered by most hosting companies can do what you are looking for as well. They give you a little more flexability and control but it also means you pretty much have to do all the website design as well. I guess it all depends what your preferences are.
With no or little tweaking, I would expect most out of the box solutions for ecommerce sites to work flawlessly, you really don't need much for what you are asking for. If after google'n it yourself you seriously can't find a solution, ask again including what solutions you tried and I'd be happy to dig deeping into one of the many carts we use.
The first one for beginners that comes to mind with many customizations is OSCommerce. The community involvement there is great, so chances are what you need is already there.