  We present a detailed, quantitative study of the competition between
interaction- and disorder-induced effects in electronic systems. For this the
Anderson-Hubbard model with diagonal disorder is investigated analytically and
by Quantum Monte Carlo techniques in the limit of infinite spatial dimensions
at half filling. We construct the magnetic phase diagram and find that at low
enough temperatures and sufficiently strong interaction there always exists a
phase with antiferromagnetic long-range order. A novel strong coupling anomaly,
i.e.~an {\it increase} of the N\'{e}el-temperature for increasing disorder, is
discovered and explained as an generic effect. The existence of metal-insulator
transitions is studied by evaluating the averaged compressibility both in the
paramagnetic and antiferromagnetic phase. A rich transition scenario, involving
metal-insulator and magnetic transitions, is found and its dependence on the
choice of the disorder distribution is discussed.
