Maybe it's just me, but if you have actual cracking in your ceiling, then there's a problem with the ceiling and putting a popcorn finish up is just going to give you.. a popcorn ceiling with cracks. My neighbor is a drywall guy and he showed me how to fix those cracks permanently. All the houses around here are 60+ years old and some of them show the age.
It's not really all that hard to do either, and I would think would take a lot less time than repainting the whole ceiling with popcorn stuff and a lot less messier. You use a special primer on the ceiling where the cracks are, put fiberglass tape over the cracks and use a special plaster mix to lay over it. Paint with the same color paint, and whoila! You should be able to get these materials at home depot. If you wanted me to ask him what the special primer and plaster mix is, PM me and I will run over and ask him. He said the thing that took the most time was waiting for the paint to dry. Lol!
Besides, since this is an apartment it'll give you the chance to practice your technique so when you get a house, you'll be a pro!