Both a and b are true (after you fill in the missing information). With two objects it's only a matter of chosen frame (or point) of reference. I'd argue that since you're on Earth, b makes more sense.
The importance of the heliocentric model comes from the fact that there are more objects in the solar system. With multiple objects you could also hold any one of them still but it makes the model much more complicated and the attraction between the objects less intuitive.
b is ruled out to a "reasonable" person because the Earth is not an inertial reference frame, but is clearly the 'rotating' frame, while the Sun is (approximately) stationary.
This is confirmed through the phenomena of stellar parallax and stellar aberration, which are only visible from Earth because of its motion. Even back in the 1573, Thomas Digges and many successors realized they could prove the Earth was in motion using parallax (though had trouble detecting it), and in 1729 James Bradley gave the first proof of heliocentrism using aberration. Both of these observations were taken as proof by the scientific world that the Earth orbits the Sun, and not the other way around.
The difference is that when we say that the Earth revolves around the Sun, it's implied that we are using an inertial reference frame. Yes, you can take whichever reference point you want, but it's not the default assumption.
The Earth and the Sun both revolve around a separate point that is roughly in between them (ignoring pesky other planets). However this additional point in space happens to be located inside of the sun, so unless you are going to throw in non-inertial reference frames for some unstated reason, "the earth revolves around the sun" is rather unambiguously the 'correct' answer.
The importance of the heliocentric model comes from the fact that there are more objects in the solar system. With multiple objects you could also hold any one of them still but it makes the model much more complicated and the attraction between the objects less intuitive.