Top three are:
Pure Silver (99.9%) k = 407 Watts/(meter degree Kelvin)
Pure copper k = 386 Watts/(meter degree Kelvin)
Pure Aluminum k = 204 Watts/(meter degree Kelvin)
k is the coefficient of thermal conductivity at 20 degrees C (room temperature). If you're looking for best bang for the buck, then copper is your best choice.

The reason metals conduct heat so well is the same reason they conduct electricity well. The best electrical conductors are also the best heat conductors. The reason has to do with the easy mobility of electrons within the crystalline structure of the metal at an atomic scale.

The slowest metal heat conductor is bismuth.