If you want to model the entire solar system, it's best to model the Sun, the planets, the asteroids, etc. with respect to the barycenter. That choice reduces the equations of motion to their simplest form. Note well: That "simplest form" is not all that simple if one chooses to incorporate relativistic effects into the equations of motion.
On the other hand, if you want to model the behavior of a single planet, and especially the inner terrestrial planets, it's best to model the planet as orbiting the Sun, with the other planets slightly perturbing the orbit of the planet in question. Stealing from an answer to a related question I wrote on physics.SE, the image below depicts the orbit of Venus about the Sun (red curve) and the orbit of Venus about the solar system barycenter (black curve). The horizontal axis is time in days from noon on 1 January 2000. The vertical axis is distance from the Sun (red curve) and distance from the barycenter (black curve).
It's pretty clear from the above graph that it is better, at least for the short term, to model terrestrial planets as orbiting the Sun. Over longer spans of time, the other planets in the solar system perturb the orbit of a terrestrial planet. The greatest of these perturbations is to make the orbit precess. The relativistic precession of Mercury is less than a tenth of the Mercury's non-relativistic precession due to perturbations from other planets.