By using the invariant method we find one-parameter squeezed Gaussian states for both time-independent and time-dependent oscillators. The squeezing parameter is expressed in terms of the energy expectation value for the time-independent case and represents the degree of mixing of positive and negative frequency solutions for the time-dependent case. A minimum uncertainty proposal is advanced to select, uniquely, vacuum states at each moment of time. We show that the Gaussian states with minimum uncertainty coincide with the true vacuum state for the time-independent oscillator and the Bunch-Davies vacuum for a massive scalar field in a de Sitter spacetime.