Any will do. I myself buy items separately and put them in my own small plastic container (MUCH CHEAPER). Band aids, peroxide, gauzes, tape, scissors, antiseptic wipes, antibiotic ointment, elastic bandage (I keep the medicine like pain relief stuff in different area)
Important thing is with your apt. is to check the fire alarms, put new batteries in them, buy fire extinguishers, and buy carbon monoxide testers if uses gas.
Congrats on your first rent! <3