Moving to a far place means shipping your items. This can be more expensive than by relocating to a different city where a simple moving truck will help you in your move. While there are moving companies that cater to overseas moving. You need to be aware that the costs are higher as compared to a regular move.
Considering how tough times are these days, it is important to save in every possible way. First way to save on shipping costs would be to decide what to bring and what to leave behind. This is important as others may just have this separation anxiety where they just cant leave their things behind.
While shipping the items on their original boxes may be the best way to go, in case when the original box is not available anymore, using the ones that are provided by the moving company will do. Make sure to label things according. Say you are moving a potted plant, make it a point to put an arrow otherwise people in the handling department may put it upside down.