This study proposes a novel learning paradigm for spiking neural networks (SNNs) that replaces the perceptron-inspired abstraction with biologically grounded neuron models, jointly optimizing synaptic weights and intrinsic neuronal parameters. We evaluate two architectures, leaky integrate-and-fire (LIF) and a meta-neuron model, under fixed and learnable intrinsic dynamics. Additionally, we introduce a biologically inspired classification framework that combines SNN dynamics with Lempel-Ziv complexity (LZC), enabling efficient and interpretable classification of spatiotemporal spike data. Training is conducted using surrogate-gradient backpropagation, spike-timing-dependent plasticity (STDP), and the Tempotron rule on spike trains generated from Poisson processes, widely adopted in computational neuroscience as a standard stochastic model of neuronal spike generation due to their analytical tractability and empirical relevance. Learning intrinsic parameters improves classification accuracy by up to 13.50 percentage points for LIF networks and 8.50 for meta-neuron models compared to baselines tuning only network size and learning rate. The proposed SNN-LZC classifier achieves up to 99.50% accuracy with sub-millisecond inference latency and competitive energy consumption. We further provide theoretical justification by formalizing how optimizing intrinsic dynamics enlarges the hypothesis class and proving descent guarantees for intrinsic-parameter updates under standard smoothness assumptions, linking intrinsic optimization to provable improvements in the surrogate objective.