Whether you buy boxes, get them for free from stores that are getting rid of them anyway, or snag them from people giving them away locally via social media, you'll need a variety of cardboard cubes for your move. If you opt for plastic bins, bear in mind you may be required to tape them all around to prevent the lid from unlatching—forgetting to do so could cause delays on moving day.
Breakable items should be bubble wrapped or covered with paper or newspaper. With extremely fragile objects, Styrofoam peanuts might also be helpful. Be sure to check if your moving company transports glass objects, like glass tabletops, in advance. If not, you may want to opt for stowing these items in the back of a personal vehicle or ditching them altogether.
Something else most movers won't transport: liquids. If you have a well-stocked bar, bottles of alcohol will need to make the move another way, as will items like cooking oils. However they're transported, special packing applications should be taken to ensure liquids don't spill or break.
It's helpful to mark boxes clearly by designated rooms, both for yourself and your movers. Denoting what's inside is also helpful for the person unpacking. This makes keeping a master list of all of your boxes and their contents incredibly beneficial.
One last packing tip: If you opt to have a moving company pack for you, take whatever you don't want packed out of the house on packing day. Leaving "Don't Pack" notes on certain items doesn't mean they won't get packed anyway. So save yourself the headache of rummaging through every single box for little necessities like remotes, power cords, and small devices by sorting those items yourself.