When I moved last year I did all the packing myself. My fabric went into cardboard boxes, lined with plastic bags. Everything was stored for about 3 months before it could be moved into the house. I had kept the original boxes for my Bernina and a middle-aged Singer, and the featherweight was in its case. The treadle and vintage Singer in a table were handled by the movers. I broke down my longarm stand, and warned the movers to pack the head very carefully in the moving van. It was wrapped in blankets and placed in a safe area. Everything came through the move okay.
If you use tubs, they shouldn't get broken, but boxes are more easily stacked and less expensive, if you don't already have the tubs.