I have used all three over the course of 30+ years as a service tech throughout the world, along with a couple of unusual methods, including the USAF, Royal Navy and US Navy. I never hesitated to ask for help.
This I have learned over a career:
Never ship anything that looks valuable by USPS. Although, I did receive my order for 22 short sub-sonics. Must have been the plain, small cardboard box and no distinguishing label or name on it.
If time is not critical, ship UPS Ground.
If time is critical, ship FedEx. UPS Next Day cost was Zone Based. If the FedEx pickup was missed, I've had the factories buy a seat on a commercial flight for my stuff a few times.
If overseas, ship DHL. They never failed me. And I have been to some really shitty places, nowhere near civilization (I was never at the edge of the world, but a couple of times you could swear you could see it.)