Labeling boxes is key
I have moved too many times to mention over the years and being a highly organized person, I became a bit of an expert. A few tips...
If you can, paint your new place before moving in. Obviously you can paint empty rooms in record time compared to moving furniture and boxes in and out of each room or trying to paint around them.
Start well in advance. Nothing worse than doing 14 hour days of packing non stop at the last minute as moving is already a very stressful process. You'll also need a tape gun.
You can get all kinds of free boxes from stores, dollar stores are best, as they have tons, pharmacies are also good. Find out what day the recycling goes out and go the day before, usually they have a bin out in the back and you can help yourself.
Liquor stores have perfect boxes for books as they have smaller strong boxes. (Do not fill up big boxes with books!)
Labelling boxes well is the Key! Especially in the kitchen where you may end up with 20 boxes for that room alone. Buy a few big black markers and keep them handy. I label "Kitchen Essentials" on the boxes with cutlery, a big knife, some dishes etc, so when I move in I can easily eat my first meal without sifting through the 20 boxes.
Label each box with a big letter(s) for the room. K for Kitchen, MB for master bedroom etc, so whoever is moving you in can place each box in the right room.
Get help. What are friends and family for? Many people moving small items such as lamps and plants etc, goes quickly and cuts down on your cost. Make sure to supply ample pizza and beer.