I happen to be one of the gardeners who like using landscape fabric, as long as it is heavy duty contractor grade. It has saved me countless hours of labor and kept my gardens looking good and almost totally weed-free. Others do not agree and that's okay.
I won't ask why you want to use stones in place of mulch. Your garden, your choice.
First, remove the existing mulch, remove any weeds, add 2 layers of heavy landscape fabric (that will keep the stones from working their way into the soil). Then use a pre-emergent such as Preen to prevent weed seeds from successfully germinating. Add an edging of some type to keep the stones in place. Then add your stones.
Not every plant likes to live with stones so I'll leave that for someone else to answer.
There are pros and cons to both mulch and stones.