One of my best tips (I have hundreds of them, but won't post them all here), is to purchase the standard-sized boxes from a moving/storage company, or even put out a request on Facebook to see about picking up ones from someone else's move. Shipping boxes from places like
Amazon, or produce boxes from the grocery store, are great, except that they come in all different sizes and don't stack well. You can fit more stuff into a POD or U-Haul or moving van when everything stacks neatly. It also protects your belongings, as items are less likely to shift.
Have a pack last/open first box with things like:
Bathroom: hand towels, bath towels, bath mat, bar soap and soap dish, shower curtain, nail clippers, cotton swabs
Bedrooms: sheets, pillows, blankets, alarm clock
Kitchen: cups, paper plates, cutlery, dish towels and cloths, paper towels
Cleaning: bucket, rags, paper towels, vacuum bags
Miscellaneous: tools for reassembling furniture, chargers, first aid kit, extension cord, portable speaker, cables for TV systems, wi-fi router, scissors, utility knife/box cutter, light bulbs for lamps, items needed for baby-proofing, flashlight (you will need to have batteries on hand to use it)
Movers will not move liquids (cleaning supplies, wine, vanilla, medicines, snow globes, condiments, etc.), batteries (remove them from all toys, flashlights, radios, remote controls, etc.), fire extinguishers and propane tanks (our moving company wouldn't, at least), and likely a whole host of other hazardous items. Make sure you know what they won't take and start eliminating them now.
Be mindful of every item you purchase, especially food. When you pay by the pound, moving cans of peaches and bags of sugar can really add up. For most of those items, it is cheaper to just buy new/fresh at your next destination. Start planning meals now that will help you use up everything ahead of time. Empty that freezer well ahead of time, so you can defrost and clean it. Be sure to keep a running list of everything you need to buy once you get to your new home, again, things like cleaning supplies, dish soap, shampoo, that got used up or not moved.
Moving companies will usually not insure particle board furnishings against damage unless they are completely taken apart and moved flat (Check the details on your contract or call to find out.) Be sure to place all of the parts into a baggie and put them into a clearly labeled "Parts Box" so that they can be found easily when you need to reassemble things.
Get a bunch of zip-top bags. Anything that has small parts, bag it. This goes for all of the pens and doodads in the junk drawer, toys with small parts, jigsaw puzzle pieces, small kitchen gadgets, etc. Little bits have a habit of getting lost in the packing paper or falling out of boxes (puzzles and board games, especially, as some packers will pack them vertically and the boxes can jiggle open).
Take the time to bundle and label cords for electronics before the movers start disassembling and packing. They all start to look alike when they are jumbled in the bottom of a box.
Have a file for all of your important documents like passports (including past expired ones that contain all of your information), birth certificates, marriage license, adoption records, bank documents, insurance information, pet records, moving contracts, medical/vaccination records, and emergency contact numbers.
I could seriously go on and on and on. I have pages of tips written out in a document that I used to share with friends that was based on all of the things we learned from our multiple moves. I could literally write a book on this topic.
