I use both the workspace email and the cPanel email depending on what I need to do. I've run online stores since 1997 - yes, that shows my age. Here's how I typically set up a store now with regard to email.
The workspace email is much like the interface to gmail and other similar services. Its easy to add a calendar and file-space if you need.
I have one email that goes to the person(s) responsible for order fulfillment (cartsales@......). Sometimes, this is forwarded to a couple of people. For example, if the order is to be completed via dropship vs. direct-ship the email goes to two people. The first is our order department to log/monitor the order and the second is straight to the fulfillment center.
I have a second email constructed for customer support. On this email, I have a person's name assigned to it so the customer doesn't think they sending an email to an unknown entity. You don't necessarily have to use your own name.
I also have a third email that works with my advertising and email list. Once again, it separates some of the functionality of advertising vs. order fulfillment.
Finally, if you're doing it all yourself you can setup forwarding email addresses to go the one that you check. This is what I typically use cPanel for.
Hope it help!