Frankly speaking there's no cheapest yet fast way for shipping as they are conflict. The shipping rates mainly depends on the product name, weight, volume, shipping country and delivery time, the more faster the more higher shipping rates, each virant is different there has a different way for shipping.
Thus for small package(under 2kg) dropshipping ShipAnt mainly ship via 4PX and Yunexpress as they usually deliver from China to EU and USA in 7 to 15 days, stable and cost effective, you can inquire ShipAnt shipping rates.