  In scalar-vector-tensor (SVT) theories with parity invariance, we perform a
gauge-ready formulation of cosmological perturbations on the flat
Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) background by taking into
account a matter perfect fluid. We derive the second-order action of scalar
perturbations and resulting linear perturbation equations of motion without
fixing any gauge conditions. Depending on physical problems at hand, most
convenient gauges can be chosen to study the development of inhomogeneities in
the presence of scalar and vector fields coupled to gravity. This versatile
framework, which encompasses Horndeski and generalized Proca theories as
special cases, is applicable to a wide variety of cosmological phenomena
including nonsingular cosmology, inflation, and dark energy. By deriving
conditions for the absence of ghost and Laplacian instabilities in several
different gauges, we show that, unlike Horndeski theories, it is possible to
evade no-go arguments for the absence of stable nonsingular bouncing/genesis
solutions in both generalized Proca and SVT theories. We also apply our
framework to the case in which scalar and vector fields are responsible for
dark energy and find that the separation of observables relevant to the
evolution of matter perturbations into tensor, vector, and scalar sectors is
transparent in the unitary gauge. Unlike the flat gauge chosen in the
literature, this result is convenient to confront SVT theories with
observations associated with the cosmic growth history.
