In this work, we study hybrid precoding techniques applied to multi-user Transmitting Reconfigurable Intelligent Surface (T-RIS) systems. The T-RIS considered here is a large array of electronically reconfigurable antenna elements illuminated by a small set of active sources. When it comes to digital signal-processing techniques applied to T-RIS systems, it is necessary to consider realistic models to bridge the gap with theoretical results. For this reason, we propose a multi-beam T-RIS propagation model with strong phase quantization constraints and limited beam codebooks. First, the proposed model is validated by characterizing a Ka-band T-RIS. Then, we optimize the quad-beam T-RIS structure by tuning the focal distance between the lens and the focal sources according to two metrics: (i) the per-user antenna gain (analog-only approach), and (ii) the per-user average rate (hybrid digital/analog approach). For both indicators, the system performance is evaluated in a multi-user scenario by assuming imperfect channel state information. We show that considering only the analog precoder is sufficient to optimize the T-RIS. However, the fully hybrid precoding scheme is required to deal with inter-user interference. We propose a codebook-aware optimization that improves the aperture efficiency of the T-RIS system.