Boxes and bags are the staple for moving - whether you're using plastic boxes and under bed storage containers, or getting cardboard ones - using suitcases, or black and plastic bags, you'll need to consider how many you need and allow for extra. You'll also need newspapers, paper, packing foam and/or bubble wrap. You'll also need tape, a marker pen and if you get them, stickers to mark your boxes.
Buying boxes and containers from hardware stores or supermarkets is a good way to get sturdy, reusable containers for your new house, but may not prove to be cost effective if you've got lots of belongings. Boxes are a good, cheap alternative to plastic containers and can be bought from websites, along with tape and stickers to mark your boxes.
Boxes are a great way to pack things into regular spaces and makes them easier to carry. You can also get boxes from supermarkets, and sometimes from recycler and on Craig’s list. Some removal firms also supply them if you're using their vans, or their moving men, or provide them if you are letting them pack for you. Packing clothes into suitcases or bags means that they are easy to transport, and easy to fit into spare spaces in your transport, but you need to make sure that the bags or cases are sturdy enough to contain your belongings well.
Cheap bags are no good if you need to use two of them or they burst when you pick them up. Snagging risks are also something you'll have to consider, as anything sharp might cause tears in your bags. Containers should all be stackable to get the most use whilst moving - or should be placed in front of your boxes so that your space is maximized whilst the move is in progress.