If the gift is small sized and you are not in a hurry, I think you can use EMS of China post, for it's cheaper but needs more time.
If you are in a hurry, you may use UPS or DHL (DHL shipping is cheaper than UPS when the gift is less than 5.5 Kg). Fedex is good for shipping to south east Asia, but for south America, its advantage is not that clear.