Be careful of the other meaning of Rayleigh scattering (the blue sky business, wavelength much longer than the particle size). For elastic scattering, the answers are:
1) yes
2) yes
3) yes
4) yes
In other words, it's not an either-or, each of these answers will work in the appropriate context. (1) means you are treating the problem classically, works fine whenever photon quantum effects aren't crucial. (2) means you are using the quantum mechanical wave function, or it could also be done classically, but it mostly means you are taking account of the coherence effects over the finite size of the target (typically only important for Mie scattering, i.e., not the Born approximation). (3) means you are contenting yourself with a rather crude particle picture, yet if you know how (1) or (2) plays out, you can then substitute picture (3) in cases where interference patterns are not of interest. (4) means you are treating both the photon and the electron quantum mechanically, and so this is the most correct way, although you have to be clear that you are using the generic meaning for "absorption" (that is, some people only use the word absorption to mean when the photon is thermalized and destroyed). By the way, Mie scattering doesn't mean it's inelastic, it means the way a wave interferes with itself is important, i.e., the size of the scatterer is not much smaller than the wavelength.