Comment by pmontra
Time ago I read that the cheapest way to do it (energy wise) is going very far away, let's say entering Pluto's or Neptune's orbits, cancel out the orbital speed there (it's lower than Earth's one) and then fall into the sun. It takes quite a bit of patience.
Right, this is a bi-elliptic transfer, which is delta-v-cheaper than a Hohmann transfer for widely separated orbits. https://en.wikipedia.org/wiki/Bi-elliptic_transfer
In practice in the real solar system, the cheapest way to get from Earth to the Sun is to use Jupiter. Launch to there and reverse-slingshot to cancel out the orbital velocity and drop directly towards the Sun. The Parker Solar Probe would have done this, although decided not to because of the complications in designing to handle both the cold of Jupiter and the heat of the Sun.