We all have them, the clear plastic tubs that you can pick up from most stores. They may be good to store your items at home, but when it comes to moving it can be a different story. When packing your items into a truck, a removalist needs to be able to stack items. Clear plastic tubs aren't always made of strong plastic and so they tend to break quite easily when stacked in a truck. If a removalist can't stack the containers then this may take up unnecessary space and may mean the removalist having to do 2 trips. Whats recommended is getting more heavy duty plastic tubs that can hold a bit more weight in them and are more structural. If you do have the clear plastic tubs then make sure they are as light as possible as they can then be stacked at the top of the truck and will reduce the likelihood of being broken in transit.
Mattress cover packs that you can pick up from your local storage facility or Bunnings are great if you are storing your items however when moving mattresses, having these covers can make it very hard to move. Mattress covers tend to be very lose, so they can fit a variety of sizes of mattress but when moving it makes it hard to grip onto the mattress and if access is restrictive when moving this can make it hard to manoeuvre your mattress. A reputable removalist will always shrink wrap your mattress which provides greater protection when moving your mattress and makes it a lot easier to manoeuvre. Shrink wrap is available from sotrage facilities and your local Bunnings as well.