Reconfigurable intelligent surfaces (RISs) consist of many passive elements of metamaterials whose impedance can be controllable to change the characteristics of wireless signals impinging on them. Channel estimation is a critical task when it comes to the control of a large RIS when having a channel with a large number of multipath components. In this paper, we derive Bayesian channel estimators for two RIS-assisted massive multiple-input multiple-output (MIMO) configurations: i) the short-term RIS configuration based on the instantaneous channel estimates; ii) the long-term RIS configuration based on the channel statistics. The proposed methods exploit spatial correlation characteristics at both the base station and the planar RISs, and other statistical characteristics of multi-specular fading in a mobile environment. Moreover, a novel heuristic for phase-shift selection at the RISs is developed. A computationally efficient fixed-point algorithm, which solves the max-min fairness power control optimally, is proposed. Simulation results demonstrate that the proposed uplink RIS-aided framework improves the spectral efficiency of the cell-edge mobile user equipments substantially in comparison to a conventional single-cell massive MIMO system. The impact of several channel effects are studied to gain insight about when the channel estimation, i.e., the short-term configuration, is preferable in comparison to the long-term RIS configuration to boost the spectral efficiency.