USPS usually has the lowest rates (unless you have heavy volume discounts from Fedex or UPS because you ship a whole lot) for that box size. I am assuming you don't have overnight or 2-day delivery needs and all that.
As a side note, we used to hear this question often from the Shopify merchants who use our Ordoro shipping app. Based on that, we recently launched a rate comparison feature that will let you lookup USPS, UPS and Fedex rates for a given package in real time, and let you pick the best method based on cost, speed etc.
This depends on the weight and dimensions of the product, but most of the time USPS stands out among the rest. USPS will almost be the cheapest option unless your package is heavy or there are any special shipments that USPS can't ship.
If you are having negotiated rates from FedEx or you want to ship heavier products, FedEx would be a good option. But, since Shopify doesn't directly handle Shopify FedEx shipping, you will have to use an app like FedEx Rates, Labels and Tracking app to handle FedEx shipping.