We have done several migrations. Our experience has been to use the following extension Aitoc Orders Export and Import:
Here are some of the limitations of the extension, all of your ported orders will not have the cc authorization info. Meaning if a customer contacts you after it is ported and you need to provide a refund, you will have to do it through the gateway or via paypal. You won't be able to do it through the system.
Ported orders serve as a reference, they won't be in any of the reports. So you start fresh with all of your selling reports.
If there are multiple items on an order, it pulls the right total but only pulls the first item on the order.
We did a magento go to a magento community port, not sure what you are doing, but just wanted to share our experience with you and your migration.