The increasing demand for network capacity is driving the development of next-generation high-speed Passive Optical Networks (PON) supporting 25 and 50 Gbps. One solution to reduce transceiver cost is reusing the 10G-class optical transmitter (including Directly Modulated Lasers, DML, in O-band) and receiver components in combination with Digital Signal Processing (DSP) techniques to compensate for bandwidth limitations. In this article, by means of both a set of laboratory experiments and a metropolitan field demonstrator, we discuss practical PON solutions at 25 and 50 Gbps per wavelength and per direction. In terms of modulation formats, we compare 2-level pulse amplitude modulation (PAM-2), 4-level PAM (PAM-4), and electrical duobinary (EDB) modulation formats, with feed-forward (FFE) and decision-feedback (DFE) adaptive equalizer at the receiver side. The novelty of our article is manifold. First, we present an optimization in terms of optical receiver band requirements for the 50 Gbps transmission. We show, by means of experimental measurements and numerical simulations, the minimum required bandwidth for DML laser and APD receiver (with appropriate DSP techniques) to realize next generation 25 and 50 Gbps PON transceivers. Second, we discuss also the upstream point of view, with a specific focus on DSP, and in particular, we propose an experimental solution based on a burst mode receiver with memory-aided DSP technique, together with a novel DSP approach to overcome the typical AC coupling distortion due to the burst mode scenario. Finally, we show a coexistence experiment between XGS-PON and 25 Gbps PON on an installed metropolitan field trial.