i had an older heavy machine mailed to me and they sender packed it very well in a double corrugated box with lots of packing peanuts. there were so many packing peanuts i actually had to dig the machine out of them to get to it but he packed it so well there was no movement of the machine inside the box. he sent it ups.
i have found fedex to have some of the highest shipping prices around. ups prices can be expensive if you ship somewhere that is not a major route like a rural off the beaten path route. i have had to ship some large bulky items through my ebay store. ebay sellers get a slight discount on rates from the major shippers. but the big thing is to pack the machine in a strong box with enough packing materials so that there is no movement of the machine. you want it to be cushioned well for the rough travels it will have and i would mark fragile handle with care on the box.