This paper presents the optimal power control policies maximizing the effective capacity achieved with arbitrary input distributions subject to an average power constraint and quality of service (QoS) requirements. The analysis leads to simplified expressions for the optimal power control strategies in the low power regime and two limiting cases, i.e., extremely stringent QoS constraints and vanishing QoS constraints. In the low power regime, the energy efficiency (EE) performance with the constant-power scheme is also determined by characterizing both the minimum energy per bit and wideband slope for arbitrary input signaling and general fading distributions. Subsequently, the results are specialized to Nakagami-m and Rician fading channels. Also, tradeoff between the effective capacity and EE is studied by determining the optimal power control scheme that maximizes the effective capacity subject to constraints on the minimum required EE and average transmission power. Circuit power consumption is explicitly considered in the EE formulation. Through numerical results, the performance comparison between constant-power and optimal power control schemes for different signal constellations and Gaussian signals is carried out. The impact of QoS constraints, input distributions, fading severity, and average transmit power level on the proposed power control schemes, maximum achievable effective capacity and EE is evaluated.