The best moving tips are in my Book "Sell Your home now..) However I am going to give you a few of my top ten here :). I've moved countless times over the years.
1.) I never use news paper, bubble wrap, etc. I use table cloths, towels, linens, blankets, sheets, recyclable plastic grocery bags, and even one moving expert said use clothes! That's genius, but I didn't think of using clothes but its a great space saver!
2.) Eat through the food in your freezer, refrigerator, and pantry. Trust me food doesn't move well especially frozen or refrigerated food, even in a close move it still can get iffy. Plus its always good to rotate food supplies to keep them fresh. Then down size what is left into marked plastic or glass holders (I just use a black sharpie). It will save you a ton of space. A 1/3 full cereal box takes up way more space than a bin that's full.
3.) Toss all expired foods and dump all expired medications at a local medication drop, usually the police or sheriffs station have one.
4.) You cant beat wardrobe boxes they are great...
5.) The best tip I learned for paint ( yes paint) is putting it in clean glass pasta sauce jars. First carefully check all paint and get rid of what is dried up, moldy, or yucky (most communities do a paint round up every so often) then start pouring away it saves so much space. Also leave what matches the home for the buyer.
6.) Sort out the instruction manuals that stay with the house plus anything else like the ceiling fan remote and leave it in a drawer taped shut and marked STAYS!
7.) Throw out all broken toys and donate out grown ones.
8.) Donate or toss old clothes
9.) Take in all recyclables.
10.) Check all kids boxes and all boxes for trash! I can't tell you how many times trash gets packed with everything else. Gross.