Most organic mulches are applied 2-4 inches thick. Rock mulches average 2-3 inches deep. Mulches applied for winterization are usually 4-6 inches deep. Whenever possible, fabric weed barriers are an excellent idea. They aren't foolproof, but they greatly reduce weeds coming from below the barrier.
Plastic is a less expensive alternative, but it greatly inhibits air and water flow.
A weed barriers will not keep seeds from germinating on top of it. Preen, a pre-emergent herbicide, is a good alternative to weed barriers. It is important to weed thoroughly before using Preen, since its job is just to keep new weeds from germinating. It does not affect anything that already has leaves or a root system. Preen can be incorporated into the soil surface or sprinkled on top of mulches and gently watered in.