The shipping company that loses the most packages is FedEx.
USPS is the second company that loses the most package.
UPS is pretty good at not losing packages although all shipping companies have and will sometimes lose packages.
FedEx, UPS and USPS and other shipping companies have insurance that can pay for any lost packages.
It's rare though for packages to go missing and most often they are eventually found and delivered.
For shipping costs the USPS is the cheapest, especially for shipments of small packages.
I've shipped a small package that costs $15.60 to ship at FedEx and the same size package and same weight package cost only $7.10 to ship with USPS using USPS ground advantage.
UPS is often more expensive to ship with than FedEx and USPS.
Small packages are often better shipped using USPS ground advantage and larger packages are better shipped through UPS or FedEx.