We develop a unified platform to evaluate Ideal, Linear, and Non-linear $\text{Pr}_{0.7}\text{Ca}_{0.3}\text{MnO}_{3}$ memristor-based synapse models, each getting progressively closer to hardware realism, alongside four STDP learning rules in a two-layer SNN with LIF neurons and adaptive thresholds for five-class MNIST classification. On MNIST with small train set and large test set, our two-layer SNN with ideal, 25-state, and 12-state nonlinear memristor synapses achieves 92.73 %, 91.07 %, and 80 % accuracy, respectively, while converging faster and using fewer parameters than comparable ANN/CNN baselines.