I`ve seen good performance hosting e-commerce sites with both 1&1
and GoDaddy. As ChristineG mentioned, host provide the space for your
website. Magento Commerce
is a great (free :) e-commerce platform that handles most of the features you mentioned.
As for the forum, you could always use an additional platform, like Vanilla or bbPress.
Some web host do offer e-commerce solutions, but they are usually light on features.
Did you find a solution?