We evaluate static properties and semileptonic decays for the ground state of doubly heavy and Xi, Xi', Xi* baryons. Working in the framework of a nonrelativistic quark model, we solve the three-body problem by means of a variational ansatz made possible by heavy-quark spin symmetry constraints. To check the dependence of our results on the inter-quark interaction we use five different quark-quark potentials that include a confining term plus Coulomb and hyperfine terms coming from one-gluon exchange. Our results for static properties (masses, charge radii and magnetic moments) are, with a few exceptions for the magnetic moments, in good agreement with a previous Faddeev calculation. Our much simpler wave functions are used to evaluate semileptonic decays of doubly heavy Xi, Xi'(J = 1/2) and Omega, Omega'(J = 1/2) baryons. Our results for the decay widths are in good agreement with calculations done within a relativistic quark.model in the quark-diquark approximation.