The ground state of NaxCoO2 (0.0<x<1.0) is studied by the local density approximation plus the Gutzwiller approach, where charge transfer and orbital fluctuations are all self-consistently treated ab initio. In contrast to previous studies, which are parameter-dependent, we characterized the phase diagram as (1) Stoner magnetic metal for x>0.6 due to a_{1g} van Hove singularity near the band top, (2) correlated nonmagnetic metal without e_{g};{'} pockets for 0.3<x<0.6, and (3) e_{g};{'} pockets appear for x<0.3, and additional magnetic instability is revealed. Experimental quasiparticle properties are well explained, and the a_{1g}-e_{g};{'} anticrossing is attributed to spin-orbital coupling.