You can't quite do it the way that you are describing there. The biggest issue is: one site = one theme. You can only have one active theme on your standard WP installation. If you want/need multiple themes, you have to have multiple installations.
But, there's bit of a way around that. You can set up different templates to work for different areas of the site. That gives you pretty much what you're after, it's just the terminology that you used was a bit wrong.
The e-commerce theme that you use will be guided by the e-commerce plugin that you use. There's no point suggesting a theme that works for one plugin when you're going to use a different one. On top of that I'd think that using the same standard theme as everyone else is goingto make you look the same as everyone else, so you'd be best off doing your own customisations to get it working and looking the way that you want it to.
Another option is also to use a Network (multisite) install and keep each part of the site completely seperated. This is a fiar bit more work and administration, but the resutls would be good if you realyl wanted the site broken up into distinct sections.