When you pack, as well as having a 'first night' box / boxes with essentials such as bedding, loo-roll etc, have a 'last day' box of the stuff you need as you go round the old house before you leave. (tea/coffee/water/soda / chocolate biscuits for yourself and the movers, cleaning stuff, vacuum cleaner etc.) a lot of this will overlap with the first things you want in the new place.
Put that box somewhere it *can't* be packed - for instance, when i moved, before the movers arrived I put my vacuum cleaner, the suitcase with my night clothes, wash bag and changes of clothes, and a box with cleaning stiff and a set of tableware into my car, and locked it, so those things wouldn't be packed by mistake. The kettle, some mugs, and tea and coffee were in the kitchen on a tray marked 'DO NOT PACK' on a giant bright red post it note.
I don't know whether it is the same in the US, but here, if you use a removal company, they will supply boxes and packing material. You pay for the boxes but the cost is refunded if you return the boxes after you have unpacked. The company I used allows up to 12 months following the move for the boxes to be returned, so there is plenty of time to unpack. (in fact, as I have plateaued with the unpacking, I need to call them to come and collect the empties I have, as the rest won't be unpacked for some considerable time. In my case, I decided to pay to have them do the packing, and they didn't charge separately for the packing paper and tape etc. I'm not sure whether they charge if they are not packing, just moving.
If any of the rooms, or any of your stuff, is unusually sized or shaped then measure in advance to check it will fit where you want to put it.
If it is practical, get any works or decorating done before you move in - so much easier in an empty house. When i bought my last house, I was staying with my parents, which was fantastic, as it meant I could continue to stay with them for about 3 weeks after I bought the house, while I had the re-wiring done, and while we redecorated, without having to worry about moving furniture around to access anything. This time, unfortunately, that wasn't an option.