Load-velocity profile (LVP) is an autoregulatory method in resistance training, yet the optimal LVP model for the free-weight jump squat (JS) remains unclear. This study therefore compared the accuracy of different LVP models and characterized their associated neuromuscular responses during the free-weight JS. In a cross-sectional, repeated-measures design, fifteen resistance-trained men first established their one-repetition maximum (1RM), and then performed free-weight JS at seven relative loads (20–80% 1RM). We compared generalized versus individualized, and linear versus polynomial LVP models. In addition, we measured mechanical outputs including peak and mean velocity, peak and mean power, and concentric phase time. Peak and mean neuromuscular activation of the vastus lateralis (VL) and medialis (VM) was measured using surface electromyography during the concentric phase. Individualized linear LVPs (R² = 0.98–0.99) demonstrated superior accuracy and less prediction error compared to generalized models (R² = 0.76–0.90), while polynomial models offered no advantage over linear models (p = 0.49–0.50). Peak and mean power was highest at 20% and 30% 1RM, respectively. Peak and mean muscle activation of the VL both peaked at 30% 1RM and decreased with increasing load. Practitioners should use individualized LVPs for accurate load prescription in the free-weight JS. Also, loads around 20–30% 1RM can induce high levels of acute mechanical power and VL muscle activation.