When you walk into an empty apartment, the list in your head is a hundred items long and it all feels urgent. It is not. Almost none of it is. Here is the honest order of what to buy first, based on what actually gets you through the first week.
1. Somewhere to sleep
Before anything else, you need to not sleep on the floor. That can be a real bed or, for a lot less, a sleeping pad and pillows. Either is fine. What matters is that night one is survivable.
2. A way to be clean
Two towels and a shower curtain. The shower curtain is the thing everyone forgets and finds out about at 6am. Clean sheets and a clean body are most of the difference between camping and living.
3. One light that is not the ceiling
Overhead light makes any room look like a waiting area. A single lamp at eye level changes how a place feels more than a piece of furniture would, for thirty dollars.
4. A way to eat
One pot, one pan, a knife, and something to eat off of. You do not need a knife block or a twelve-piece utensil set. You need to be able to cook one real meal and wash up after.
5. Trash bags
You will fill three of them on day one. Everyone does.
That is the whole starter list. Everything else can wait until you have had a week of actual sleep and know what you reach for. If you want it decided for you, The First Night kit is exactly this list, itemized to the dollar.