We investigate the thickness dependence of the magnetic anisotropy and dynamic magnetic response of ferromagnetic NiFe films. We go beyond quasi-static measurements and focus on the dynamic magnetic response by considering three complementary techniques: the ferromagnetic resonance, magnetoimpedance and magnetic permeability measurements. We verify remarkable modifications in the magnetic anisotropy, i.e. the well-known behavior of in-plane uniaxial magnetic anisotropy systems gives place to a complex magnetic behavior as the thickness increases, and splits the films in two groups according to the magnetic properties. We identify magnetoimpedance and magnetic permeability curves with multiple resonance peaks, as well as the evolution of the ferromagnetic resonance absorption spectra, as fingerprints of strong changes of the magnetic properties associated to the vanishing of the in-plane magnetic anisotropy and to the emergence of non-homogeneous magnetization configuration, local anisotropies and out-of-plane anisotropy contribution arisen as a consequence of the non-uniformities of the stress stored in the film as the thickness is increased and/or to the columnar growth of the film. We interpret the experimental results in terms of the structural and morphological properties, quasi-static magnetic behavior, magnetic domain structure and different mechanisms governing the magnetization dynamics at distinct frequency ranges.