In ShipperHQ, we often hear that users want to sort their shipping rates from cheapest to most expensive. Other users would rather display the cheapest rate and not have the other rates displayed. This article should have all the information you need to discern the difference between the two.
So once you have rate shopping enabled (see below) then you can start creating merge rules in ShipperHQ where you could highlight FedEx Ground and UPS ground for example and ShipperHQ will choose the cheaper of the two and only display this rate.
Check here for more information on how to enable Rate Shopping.
Sorting Based on Price
If you navigate to Carriers > Settings > set “Display Rates under Generic Carrier” to YES . From there, you should see the dropdown for “Sort Shipping Methods based on Price”, allowing you to sort price based on ascending/descending order.