Again, this depends on how you define both "best" and "fitness". What's best depends a lot on what someone enjoys. I would rather do an activity I enjoy for 40 minutes than get the same benefit doing something I hate for 20. Likewise, fitness means different things to different people and at different times. You may be focusing on cardio-vascular fitness, or on strength, or speed, or weight loss, or performance in a particular sport...

Or, you know, "do something". Throwing a bunch of complexity and equipment cost at someone who doesn't currently exercise at all isn't likely to help anything much. Pushups and situps require only a clear stretch of floor.

Sure! If you're just getting started and can stick with that, maybe that's best for you! Just not for everyone.

I think calisthenics are great, but they focus more on muscular strength than cardiovascular.

There are only so many push-ups you can do before your muscles are fatigued. Running, swimming, and cycling are better for cardio because you can do them for great lengths of time.