Equilibrium is not a postulate is precisely defined condition, that of no average change in any physical quantity of interest. Nor is it specifically confined to statistical mechanics.
You should revise the terms dynamic equilibnrium, static equilibrium, stable equilibrium, unstable equilibrium, metastable equilibrium before proceeding.
The principle of a priori probabilities means that a system will inhabit every state available to it in accordance with the statistical weight of that state, if we observe it for long enough.
A state is a particular set of values of the properties of interest.
A good easily readable introduction is offered in
Statistical Thermodynamics by Andrew Maczek