The checkout process can be a bit odd.
What I have done is disable the emails related to not finished.
When an order has successfully had payment submitted, the order is set as processed and an email is sent to the staff and the customer.
The order then remains as processed until it ships. At which point, it is marked as complete and an email is sent with the tracking information.
At this point, we are only using Paypal standard, which means that we accept payments from paypal accounts and from debit/credit cards (using Paypal).
We are anticipating switching to Paypal advanced as soon as all of the issues have been worked out with it on the x-cart side.
Hopefully that helps
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