Wait on decor items until youmove in and see what the lighting is like. Also wait on things that go inside the pantry or closets like trash cans since you don't know the dimensions of the space and might end up with something too big.
For utility items:
1. Step stool.
2. Shower caddy for over the shower head.
3. Shower liner (you can wait on the curtain) and rings. Get a long tpye so you can be sure it will go deep enough into the tub.
4. Key rings for your new keys.
5. Toilet paper, paper towels, plastic utensils for move-in day when everything else is in boxes.
6. Fire extinguisher - ABC/multi-purpose.
7. Renters insurance (if a disaster occurs in the building, the landlord's insurance will cover that damage to the building structure and components. However, they will not cover any of your items that get damaged (clothing, electronics, valuables, food, decor items, etc.. You need renter's insurance for this. It's like home owner's insurance, but for people who rent apartments or houses.)