In a 20ga, #3 buck is most common but you can find #2 buck in some shops. I suggest #2 if you can find it. At short distances of smaller apartments/homes used for student housing, your pattern spread isn't going to be much. Rooms are what, 10x12 feet or 10x15? What's the longest range you'd have to cover? Perhaps 20-25 feet?
In 12ga you have more options. I'd suggest #4 buckshot for lower wall penetration or #1 Buckshot if necessary. If nothing else #00 buckshot. All these loads should be standard 2-3/4" loads (not 3" magnums). Low-recoil preferred.
It will be especially important to find a way to secure your shotgun
against theft. That means more than just hiding it. Follow the link above to see one solution.
Even if you hide it, it does no good if you (or a roomie) let's it be known that you have a gun of any kind. Keep it to yourself. And while you're at it, don't forget you'll have to conceal those ammo boxes and/or spare shells. Nothing tells a thief you have a gun somewhere like finding the ammo. The same applies when you dispose of the shipping box for the gun. Cut it down and tape the pieces together with the logos and descriptions facing inside to prevent dumpster divers from finding it.