As for buying stuff, here's my go-to list of things people should have in an apartment:

Renter's Insurance

2 fire extinguishers (one for the kitchen and one for the bedroom. Make sure the fire alarms are in working order.

Chain lock or dead bolt that can't be accessed from the outside of the door

A decent tool kit (Vice grips, 2 screwdrivers, hammer, drill, flashlight etc.)

First aid kit

Toilet plunger

Touch up paint that matches the trim