We report a state-of-the-art photoemission (angle-resolved photoemission spectroscopy) study of high quality single crystals of NaxCoO2 the series focusing on the fine details of the low-energy states. The Fermi velocity is found to be small (<0.5 eV A) and only weakly anisotropic over the Fermi surface at all dopings, setting the size of the pair wave function to be on the order of 10-20 nm. In the low-doping regime, the exchange interlayer splitting vanishes and two-dimensional collective instabilities such as 120 degrees -type fluctuations become kinematically allowed. Our results suggest that the unusually small Fermi velocity and the unique symmetry of kinematic instabilities distinguish cobaltates from most other oxide superconductors.