Fast electrons generated via the interaction of ultra-intense laser pulses with a solid target can produce multi-MeV ions from laser-induced plasmas. These fast ions can be used for various applications ranging from the ion implantation to the stimulation of nuclear reactions. The most important point here is the efficiency of production of such fast ions. We analyse in detail, with the help of an analytical model and particle-in-cell simulations, the most efficient acceleration mechanisms including the ponderomotive force driving and acceleration by the shock wave, and compare the electrostatic ion acceleration at the front side and at the rear side of a foil target. We also determine the optimal plasma density distribution shaped by the laser pre-pulse.