order submitted, status is set as pending and payment is authorized
order invoiced, status is set as processing and payment is captured
order shipped, status is set as complete and payment is still captured

Some stores will vary slightly on the first order status depending on what they have specified in their payment method as the default status for a new order. If the desired status is not available to the payment method, you’ll need to assign the status (generally pending or processing) to the state (processing).