Seriously paying movers is key. Then you don't have to worry about older family members injuring themselves, destroying your furniture, walls, etc. It will be 600 bucks or so, but it will be worth it to end the torture of moving stuff from point A to point B. So pack in advance, hire movers to come, baby is entertained by nanny out of the home while the move occurs.
Have your family go to your new place to clean before movers arrive, so pack up your cleaning supplies in a clear place, set aside. You stay at your old place to meet the movers and provide direction. Then you switch; once movers are out of your old place, you go to new place to direct them where to put things, while your family cleans out your old place, spackles holes (if you have holes from pictures, grab some spackle from target or home depot plus a putty knife and some sandpaper), uses magic eraser on wall marks, grabs anything leftover, etc. Then family comes to help you unpack the new place (as PP noted, do baby's room first). Have someone in charge of assembling the crib; someone puts away baby toys/clothes; someone unloads your kitchen stuff and food. Those are the priorities.
FYI if you have movers, you can leave clothes in dressers and just use painters tape to hold the drawers shut. It's a benefit of having really strong guys

and makes the unpacking easier!