  We apply numerical simulations to study the criticality of the 3D Ising model
with random site quenched dilution. The emphasis is given to the issues not
being discussed in detail before. In particular, we attempt a comparison of
different Monte Carlo techniques, discussing regions of their applicability and
advantages/disadvantages depending on the aim of a particular simulation set.
Moreover, besides evaluation of the critical indices we estimate the universal
ratio $\Gamma^+/\Gamma^-$ for the magnetic susceptibility critical amplitudes.
Our estimate $\Gamma^+/\Gamma^- = 1.67 \pm 0.15$ is in a good agreement with
the recent MC analysis of the random-bond Ising model giving further support
that both random-site and random-bond dilutions lead to the same universality
class.
