Kettlebells. They can be stored under a bed, brought out and used in a tiny little patch of space, and returned to their starting place at the end. They will cost a little money up front but they’re an indestructible piece that you’ll have forever. You also can get a heck of a workout in a short amount of time (some examples provided below).
I would probably start with a 25 pounder and a 35 pounder (my fiancee started out with a 25, but quickly surpassed that and now does most of her work with a 35 and a 45 pound KB). You may eventually need a heavier weight, but that should get you started.
What to do with your kettlebells, you ask? Swings, goblet squats, and get-ups would be a good start. Here are some great articles from this site on the respective movements: