This paper investigates beamforming strategies for integrated sensing and communication (ISAC) systems, where shared signal resources are employed for these services. The proposed framework focuses on maximizing the signal-to-noise ratio (SNR) of the target echo while satisfying the communication rate requirement. Addressing the challenges posed by the higher peak-to-average-power ratio (PAPR) of communication waveforms than sensing waveforms, we provide a detailed analysis and offer valuable insights into power assignment techniques that account for PAPR considerations. We reveal that the integration of constant-modulus sensing signals results in a substantial enhancement in sensing SNR, and numerical results underscore the effectiveness of leveraging sensing signals within the ISAC framework. These findings highlight the potential for achieving superior sensing performance by using dedicated constant-modulus sensing signals.