PAR-constrained sequences are widely used in communication systems and radars due to various practical needs; specifically, sequences are required to be unimodular or of low peak-to-average power ratio (PAR). For unimodular sequence design, plenty of efforts have been devoted to obtaining good correlation properties. Regarding channel estimation, however, sequences of such properties do not necessarily help produce optimal estimates. Tailored unimodular sequences for the specific criterion concerned are desirable especially when the prior knowledge of the channel is taken into account as well. In this paper, we formulate the problem of optimal unimodular sequence design for minimum mean square error estimation of the channel impulse response and conditional mutual information maximization, respectively. Efficient algorithms based on the majorization-minimization framework are proposed for both problems with guaranteed convergence. As the unimodular constraint is a special case of the low PAR constraint, optimal sequences of low PAR are also considered. Numerical examples are provided to show the performance of the proposed training sequences, with the efficiency of the derived algorithms demonstrated.