Having the right moving supplies naturally make your move flow much smoother and much more efficient - they let you do most, if not all of your tasks well and make things much easier for you.
One essential and basic supply that you must have a re boxes of course. Boxes come in different sizes - make sure to use the appropriate boxes for your things and do not force something to it in a box when it doesn't. Improper boxing and packing can increase the chances of your stuff getting damages - even to a point that is beyond repair - during the transport stage. Another tip for boxes is to try to buy used - but usable, of course - boxes so you do not only save a bit of money, you also help make your move much greener. You can also rent plastic moving boxes that are sturdier and of course, since they are only for rent and reusable, it's another good way to go for a green move, besides the fact that renting these boxes are also much cheaper.
Of course, let's not forget items such as packing tape and padding / cushions for your things such as packing peanuts and bubble wrap - the last two being very useful when packing your breakable things.