There is really no reason NOT to start at least a month in advance, if at all possible. It will really reduce your stress level!
Some things you can do about a month before the move are:
Order your moving supplies. This way, you can get a jump start on your packing, as time allows. Go into rooms you don't use a lot and start to pack them up. Maybe think about using paper plates and plastic utensils, so you can pack up your real ones. As you fill up boxes, move them to an empty room (ie basement) or a storage unit, like a Pod.
Obtain and fill out change of address forms. Make a folder of all the forms (and/or a list of websites) you'll need in order to do so, so you can do this as time allows.
-- Gather medical records from family physicians, specialists, dentists, etc.
-- Find a pharmacy near your new home and transfer prescriptions.
-- Establish a checking account at a bank in your new town.
-- Use up food items so there is less to pack, throw away, or spoil.
And, some things you can do a week or two before the move are:
-- Set up utility services at your new address.
-- Provide your new address to regular service providers (electric, water, publishers, telephone and cable companies).
-- Close bank accounts and have your funds wired to your new bank. Make sure there are no outstanding checks or automatic payments that haven't been processed.
-- Collect your valuables from your safe-deposit box.
-- Check with your insurance agent to ensure you'll be covered through your homeowner's or renter's policy during the move.
-- Defrost freezer and refrigerator.
Yes, you'll have to spend money on these items, but it's money well spent. You'll save a ton; you can avoid having to replace items that get broken and damaged during your move because they were improperly packed. Two good choices:
Lightweight wardrobe box -- use it as a temporary closet, which can be easily loaded on a truck or container. it will eliminate packing clothing in suitcases, so they can be one of the last things you pack, and can later be used for storage. Just take your clothes out of your closet, and hang them on the bar right inside the box. But, one note - don't put shoes at the bottom, or it will get too heavy.
Bubble wrap is great for packing fragile items, like dishes (which you should use a stronger box for, and put the dishes on the bottom, with some glasses on top).
And, even if you have the best tools available, you'll still need to pack properly. So, properly tape-up your boxes and always remember not to over-pack, otherwise, the box could expand and give way at the bottom. On the flip side, don't under pack a box, otherwise the contents can move around and break. You can prevent this by adding a filler, like bubble wrap or tissue paper.
Mark your boxes as you pack - include the room they should go to in your new home, and a list of what's inside. This will make it easier for you to load and unload your truck. And, it will make unpacking a lot easier, too. It allows you to make sure the correct boxes are in the rooms that they should be unpacked in, and you can identify essentials that will be needed immediately at the new home.
Optimize your space in the moving truck by not leaving anything empty. If you are taking your washer and dryer, put their hoses or your comforter in them. The fridge and vacuum bags are also great places to stash things. If you have a house, use your big trash cans, and pack up stuff from the garden (hose) or garage (paint cans, tools, cleaning solvents) that could leak through a box.
Prep your home for the move: To prevent damage to your home and belongings, take off doors (this makes it easier to get things in and out), wrap your banisters, put floor runners down. Don't wait until moving day to do this, or you'll have one more thing to be stressed out about. There's no reason you cant wrap your couch in saran wrap a couple of days before the move.
Gather all your larger items in one centralized space and determine from there the most effective way to pack a truck or container. This method will enable you to consider height, weight and size in determining the best way to pack and will eliminate shuffling and moving items once they are in a container or truck.