We present a start-to-end 3D numerical simulation of a hybrid scheme for the acceleration of protons. The scheme is based on a first stage laser acceleration, followed by a transport line with a solenoid or a multiplet of quadrupoles, and then a post-acceleration section in a compact linac. Our simulations show that from a laser accelerated proton bunch with energy selection at ~ 30MeV, it is possible to obtain a high quality monochromatic beam of 60MeV with intensity at the threshold of interest for medical use. In the present day experiments using solid targets, the TNSA mechanism describes accelerated bunches with an exponential energy spectrum up to a cut-off value typically below ~ 60MeV and wide angular distribution. At the cut-off energy, the number of protons to be collimated and post-accelerated in a hybrid scheme are still too low. We investigate laser-plasma acceleration to improve the quality and number of the injected protons at ~ 30MeV in order to assure efficient post-acceleration in the hybrid scheme. The results are obtained with 3D PIC simulations using a code where optical acceleration with over-dense targets, transport and post-acceleration in a linac can all be investigated in an integrated framework. The high intensity experiments at Nara are taken as a reference benchmarks for our virtual laboratory. If experimentally confirmed, a hybrid scheme could be the core of a medium sized infrastructure for medical research, capable of producing protons for therapy and x-rays for diagnosis, which complements the development of all optical systems.