that's a pretty tall order, and there's no way you'll find out anyway. We all have our likes and dislikes, and to be perfectly honest I've not found any one hosting company that is perfect in every way.
Hosting a business web site isn't that difficult, and you'll find hundreds of companies who will provide the necessary facilities. If it doesn't work out you can transfer your domain name to a new host without too much difficulty, and your site visitors will not even notice.
When it comes to e-commerce it can be a different story, and a great deal depends on your particular business requirements. There are many shopping cart applications, and once again different web designers favour different systems. My particular favourite is Actinic
click here It's not cheap, and it has a reasonably steep learning curve, but in my opinion (one that's shared by many) there's nothing to touch it for really professional e-commerce sites.
I have no experience of the 1&1 solution, apart from the fact that I received the same email as you, but they're offering a 30 day free trial, so you have nothing to lose by experimenting.