We predict weekly telephony contact for Centrelink customers using longitudinal administrative data aligned to a weekly grid, comparing statistical, machine learning, and deep learning models on 889,879 customers (150 features; 3.65M observations after class balancing; 5-fold CV). Feature-engineering regimes spanned from quick encodings to contact-history windows of 1, 4, 8, and 12 weeks; an 8-week history yielded the best trade-off, with diminishing returns beyond 8 weeks. Across 12 models, a Multilayer Perceptron attained the strongest performance on held-out data (AUC ≈ 0.84; accuracy ≈ 0.79). One-factor-at-a-time hyperparameter searches produced modest, non-monotonic gains, underscoring that additional tuning effort does not necessarily translate to uplift in model performance. To guide modelling investment and effort decisions, we introduced a cost-based budgeting equation associated with treatment applications of the predictive model. This framework approach encourages monetary costings to be considered alongside predictive performance for model development.