Symbiotic Backscatter Communication (SBC) has emerged as a spectrum-efficient and low-power communication technology, where backscatter devices (BDs) modulate and reflect incident radio frequency (RF) signals from primary transmitters (PTs). While previous studies have assumed a circularly symmetric complex Gaussian (CSCG) distribution for the BD's signal, this assumption may not be practical because the high complexity of generating CSCG signals is not supported by the low-cost BD. In this paper, we address this gap by investigating SBC for two low-complexity modulation schemes, i.e., $M$-ary amplitude-shift keying (MASK) and $M$-ary phase-shift keying (MPSK), where BD's signals inherently deviate from CSCG distribution. Our goal is to derive the achievable rate of the PT and BD under the MASK/MPSK and to design MASK/MPSK modulation scheme for maximizing the PT's rate. Towards this end, we first derive the expressions of both the PT's rate and BD's rate. Theoretical results reveal that whether or not the BD improves the PT's rate depends on the phase of MASK/MPSK modulation, while the BD's rate is independent of this phase. We then formulate two optimization problems to maximize the PT's rate by adjusting the phase under the MASK and MPSK modulation schemes, respectively, and derive the optimal phases for each modulation scheme in closed forms. Simulation results demonstrate that the optimal phase of MASK/MPSK can ensure an improvement in the PT's rate, and reveal that a low-order ASK modulation is better than a low-order PSK for the BD in terms of improving PT's rate, especially when the direct link is not significantly weaker than the backscatter link in SBC.