In massive MIMO systems, fully digital precoding offers high performance but has significant implementation complexity and energy consumption, particularly at millimeter frequencies and beyond. Hybrid analog-digital architectures provide a practical alternative by reducing the number of radio frequency (RF) chains while retaining performance in spatially sparse multipath scenarios. However, most hybrid precoder designs assume ideal, infinite-resolution analog phase shifters, which are impractical in real-world scenarios. Another practical constraint is the limited fronthaul capacity between the baseband processor and array, implying that each entry of the digital precoder must be picked from a finite set of quantization labels. To minimize the sum rate degradation caused by quantized analog and digital precoders, we propose novel designs inspired by the sphere decoding (SD) algorithm. We demonstrate numerically that our proposed designs outperform traditional methods, ensuring minimal sum rate loss in hybrid precoding systems with low-resolution phase shifters and limited fronthaul capacity.