We consider electronic transport through semiconducting nanowires (W) with spin-orbit interaction (SOI), in a hybrid N-W-N setup where the wire is contacted by normal-metal leads (N). We investigate the conductance behavior of the system as a function of gate and bias voltage, magnetic field, wire length, temperature, and disorder. The transport calculations are performed numerically and are based on standard recursive Greens function techniques. In particular, we are interested in understanding if and how it is possible to deduce the strength of the SOI from the transport behavior. This is a very relevant question since so far no clear experimental observation in that direction has been produced. We find that the smoothness of the electrostatic potential profile between the contacts and the wire plays a crucial role, and we show that in realistic regimes the N-W-N setup may mask the effects of SOI, and a trivial behavior with apparent vanishing SOI is observed. We identify an optimal parameter regime, with neither too smooth nor too abrupt potentials, where the signature of SOI is best visible, with and without Fabry-Perot oscillations, and is most resilient to disorder and temperature effects.