This work presents a detailed analysis of the impact of a rear point-contact (PC) scheme and a selective emitter (SE) design on the performance of a crystalline silicon (c-Si) back contact-back junction (BC-BJ) solar cell featuring narrower highly-doped back surface field (BSF) areas and wider lowly-doped emitter areas. The analysis was performed both through light and dark J-V simulations by using a rigorous full three-dimensional (3D) electro-optical modeling approach to accurately include the 3D effects of several competing physical mechanisms occurring in a PC structure. Simulation results show that the adoption of a relatively thick and wide metallization contacting the silicon at the rear side only via small circular-shaped holes gives an efficiency improvement above 0.3%abs with respect to a conventional BC-BJ solar cell featuring a linear-contact (LC) metallization scheme. Moreover, the introduction of an optimized SE design, featuring a local deeper highly-doped (HDOP) profile underneath rear point contacts and a narrower lowly-doped (LDOP) profile at the non-contacted rear interfaces, can lead to a further efficiency enhancement of about 0.2%abs, which increases with the emitter width.