I don't have experience with the specific types of home cardio equipment you're looking for, but I do have versions of all three and have some food for thought for you:
Treadmill might create a major noise issue (thumping) for your neighbors unless you're in the ground floor apartment. From my own experience, I found a treadmill to be harder on your feet and ankles than walking outside so save your money there.
I have a recumbent bike, not a spin bike. Easy to move, doesn't take up outrageous amounts of space as long as you can crank up the resistance you can get a pretty good burn going.
IMO the best cardio is an elliptical but do NOT get a low quality elliptical, first, it's less ergonomic and second, you'll destroy it in no time flat with regular use. Mine has a magnatronic back wheel (or whatever they called it). It has a big footprint and is a bit of a bear to move but despite being realatively old (6 years) it's still going strong.