Neuromorphic computing based on artificial synapses requires devices capable of gradual, repeatable, and energy-efficient conductance modulation. Ionically gated transistors are promising candidates because their ion dynamics naturally produce synaptic behavior under low-voltage operation. However, how key device characteristics—conductance range, number of accessible conductance states N, and weight-update nonlinearity β—jointly influence neural network performance remains insufficiently understood. Here, we investigate MoS2-based ionically gated synaptic transistors using a combined experimental and modeling framework that links device physics to hardware-aware artificial neural network (ANN) simulations across image-classification tasks of varying complexity. We show that under fixed-amplitude pulsing, increasing N introduces a fundamental trade-off: finer weight resolution is accompanied by stronger update nonlinearity. ANN simulations further reveal that, within the nonlinearity range studied here, classification accuracy is governed by a task-dependent optimal weight resolution rather than a simply maximized number of states, and is relatively insensitive to conductance range when N is fixed. To overcome the nonlinear weight updates, we employ a physics-informed transient model to develop a predictive pulse-engineering algorithm and experimentally demonstrate that it can linearize synaptic weight evolution in the same device. These linearized updates improve ANN accuracy by up to 7% at equivalent state resolution, establishing a quantitative link between device-level dynamics and neural network performance in ionically gated synaptic transistors.