Ok. Isotope 2.x comes with the Notification Center by default. It's a bit complicated, unfortunately the manual still has not been translated to english yet. I'll try to outline the basic steps:
Under Notification Center - Gateways you need to create a basic Email Gateway. Simply create a New gateway there, name it "Email" and set the type to Standard email gateway, then Save and close it.
Under Notification Center - Notifications create a New notification, set the title to something that is suitable for your case (e.g. "Message to admin on complete order") and set the type to Order status change. You can leave the rest on its default values. If you want to also attach a document to the Email (e.g. the invoice), you need to select that under Document. Now click Save and edit.
A notification can consist of multiple individual messages. Each message can have multiple languages defined, one language is defined as the fallback.
When editing a notification, you create a New message. Set the title to something suitable (e.g. "Message to admin on complete order" again) and the Gateway to your previously defined Email. Now click on Manage languages and add a New language. Set your desired primary language and set it as the fallback. Now set the rest of the options as you like. For instance, set the Recipients to the email address of the admin, set an apropriate subject and, sender name, sender address, etc.
Within the message text field, you have access to multiple "simple tokens", which will be replaced with their actual values. If you insert one '#' there, you will get a pop up displaying all the available simple tokens.
After you have created the notification, go to Store configuration - Order status and edit the order status for which you want to send this notification, e.g. the default "Complete" order status. Under E-Mail Notification - Notification set the previously created notification (e.g. Message to admin on complete order).
Note: if you also want to send an Email to the buyer when the order status reaches "Complete", you simply have to create a new message within this notification.