Using a six-band k · p Hamiltonian for wurtzite lattice, we study the hole ground state symmetry and composition in spherical quantum dots and elongated quantum rods made of CdS and CdSe. The ground state crossovers which occur when changing the nanocrystal size and shape are well understood in terms of hole band mixing. Contrary to previous belief, the quantum rod ground state crossover with increasing length is shown not to occur at a fixed aspect ratio. The geometry and composition that maximize the spin purity and the intensity of linearly polarized light emission are elucidated. The six-band wurtzite Hamiltonian results for CdSe are compared to those obtained with quasi-cubic four-band and one-band Hamiltonians, and the performance of these simplified Hamiltonians is discussed