Why is lanthanum a lanthanide and actinium an actinide?
According to www.webelements.com, "There is no one single or best structure for the periodic table..." 

I believe that the table was split at lanthanum since it kept the elements of the d orbitals together. You could argue that the table should be split with Sc, Y, La and Ac together, with the elements Ce through Lu and Th through Lr as the f orbital elements. The next column would have Ti, Zr, Hf and Rf.

Actually, all elements have f orbitals, below lanthanum they are not usually populated. Lanthanum is the first element that could have an electron in the f orbital in the ground state. Since the transition energy of the electron between in the d orbital and the f orbital is quite low, there should be a significant number of electrons occupying the higher energy orbital, even at room temperature.