I have moved a bunch of time over the past decade and the one thing that I'd emphasize is that things take longer than you expect and things will go wrong. Make sure to plan some buffer, so for example if you must move in during weekdays (a constraint I had once) plan to move in Monday, not Friday, since that gives you extra days to move.
If you can afford it, pay for movers *and* packers. Packers will help you put things in boxes and wrap things up safely. I did this last time I moved even though I was not moving very far. Taking trips to move fragile things yourself ahead of time if you are moving close is not a bad idea, but in my experience it doesn't save as much time as you might expect. If you can bring yourself to, get rid of anything *before* the move, so that you don't spend time and effort moving stuff, only to get rid of it from your new place. Try to have the kids at a friend or family member's house, as they are likely to be in the way and will slow you down a lot.