A common and useful criteria used for creating shipping rules in Shiptheory is to use shipping methods pulled through from the channel. 

This is an option from Brightpearl when sending to Shiptheory, and the first step will be to create said shipping methods on the Brightpearl side. Brightpearl have published a guide specifically regarding how to do this which can be found here.

After completing this in Brightpearl, the next stage will be to go back to the Shiptheory website and access your Brightpearl settings page, found in your main dropdown here:

You'll then simply want to re-save your details on the page:

After this, you should find that this new shipping method will be available to select in your Shiptheory rules:

If you run into any issues at all, or have any other questions, please feel free to contact support.