We study the classical and quantum Starobinsky model in a Jordan-Brans-Dicke-type theory. At the classical level we describe inflationary attractors. Expressions for the density perturbations and initial amplitudes for gravitational waves are obtained. At the quantum level, the Hartle-Hawking and the tunneling boundary conditions for the wave function of the Universe are determined. These wave functions are used for determining probability distributions for the initial state of the model.