Isotropic and anisotropic magnetic behavior of the frustrated spin-chain compound beta-TeVO4 is reported. Three magnetic transitions observed in zero magnetic field are tracked in fields applied along different crystallographic directions using magnetization, heat capacity, and magnetostriction measurements. Qualitatively different temperature-field diagrams are obtained below 10 T for the field applied along a or b and along c, respectively. In contrast, a nearly isotropic high-field phase emerges above 18 T and persists up to the saturation that occurs around 22.5 T. Upon cooling in low fields, the transitions at T-N1 and T-N2 toward the spin-density-wave and stripe phases are of the second order, whereas the transition at T-N3 toward the helical state is of the first order and entails a lattice component. Our microscopic analysis identifies frustrated J(1)-J(2) spin chains with a sizable antiferromagnetic interchain coupling in the bc plane and ferromagnetic couplings along the a direction. The competition between these ferromagnetic interchain couplings and the helical order within the chain underlies the incommensurate order along the a direction, as observed experimentally. While a helical state is triggered by the competition between J(1) and J(2) within the chain, the plane of the helix is not uniquely defined because of competing magnetic anisotropies. Using high-resolution synchrotron diffraction and Te-125 nuclear magnetic resonance, we also demonstrate that the crystal structure of beta-TeVO4 does not change down to 10 K, and the orbital state of V4+ is preserved.