We present the results of the optimization of a recently established atomic orbital basis set for ab initio calculations of molecules in strong magnetic fields. The optimization is performed for the ground and many low-lying excited states of the hydrogen atom in the presence of a magnetic field of arbitrary strength. The behavior of the nonlinear variational parameters of the atomic orbitals is discussed as a function of the held strength. In order to demonstrate the suitability of our atomic orbital basis set for the calculation of molecular spectra and wave functions in a uniform magnetic held we present, as first results of a molecular calculation, electronic potential energy curves for the H-2(+) ion in a magnetic field.