Moving is expensive, so it's understandable that you'd want to try and save money wherever you could. If you can move house using only your own muscles and some help from family and friends, great. But if you have to hire movers, it's never a good idea to go with a discount company unless their work has been vouched for by someone you know who has used their services before. The reason for this is that your things may not survive the trip unless you're there to constantly hover over their shoulders supervising their work.
One of the most important things to look for in a moving company is insurance. If the company will not guarantee your valuables will arrive intact, choose another company. Without the threat of an insurance payout over their heads, many movers may not be motivated to take adequate care of your belongings. Frequent complaints about moving companies include handling boxes roughly, stacking heavy boxes on top of fragile ones, and failing to secure the load inside the truck so it doesn't move around during transit. In fact, many people choose to take their most valuable items in their own cars during the move. The moving company should have blankets to cushion your furniture, but all the same it may be a good idea to leave your old blankets unpacked for added protection.
In cases where the move is cross country or international, it may not be possible for you to move things yourself. You will have to hire a freight carrier to take your belongings by boat or plane to your new home. As with a moving truck, always get your items insured for their full value. You can also help your items survive the trip by packing them carefully into a box, making sure they are cushioned and that the extra space is filled with packing peanuts, bubble wrap, or balled newspapers. Boxes should be sturdy and flaps should be tucked and taped to avoid bottoms falling out. Where boxes will be conveyed by boat, waterproofing your items by storing them in seam taped corrugated plastic containers is a good idea.