While the ideal travel for the machine is in your own car, life is sometimes not accommodating. If you are forced to ship it with your household goods. I would double box it. While using fabric might sound good as well as economical it is also very heavy and will add to the weight. Also movers tend to put the heaviest things at the bottom of the pile
If forced to pack it, I would first wrap it in several layers of bubble wrap / put it in a box with a little bit of room in it and fill that box with packing popcorn / then find another box at least 6 to 8 inches larger in all directions / put several inches of popcorn in the bottom of the larger box / center the box containing the machine / fill the rest of the larger box with more popcorn and tape it well.
Mark it well with Fragile stickers and I would be tempted to write on it some sort of request not to stack things on top of it.
I used this method when we moved ten years ago for extremely fragile things including my serger. By double boxing it - the machine can not shift or settle to the bottom. Everything in our move arrived in perfect condition including the serger. Good Luck!!