I'm more than positive I'm just missing something (I've only been with Invision for a few weeks), but how do you change the order status (in progress, delayed, complete, etc.) of a client order? Is this possible from the "orders" page, or from the Admin CP? If not, is there a plugin out there anyone is using they can recommend to me? I appreciate the help!

Are you talking about shipment orders? If so, they do not have multiple separate statuses. You can adjust from pending to shipped to cancelled, but cannot define custom statuses like "in progress". That's not a bad suggestion though, so you may wish to post in our Feedback forum requesting this change be added in a future release.

Actually, I would mainly be providing "services" in the form of consultation and digital files. So, non-physical items would be the main type of product offered. Maybe that's why I don't see the options you've listed. I will definitely list this as a suggestion, thanks @bfarber!