The emergence and the evolution of the metallic charge transport in the La2-xSrxCuO4 system from lightly to optimally doped samples (x = 0.01-0.17) are studied. We demonstrate that in high-quality single crystals the in-plane resistivity shows a metallic behavior for all values of x at moderate temperatures and that the hole mobility at 300 K changes only by a factor of 3 from x = 0.01 to 0.17, where its x dependence is found to be intriguingly similar to that of the inverse antiferromagnetic correlation length. We discuss an incoherent-metal picture and a charged-stripe scenario as candidates to account for these peculiar features.