That would work for a while but over time those unwanted plants will return. "Weed" control is not a one time job but a continuous one. Weed barrier cloth can help suppress some "weeds" for a time but as many of us have found t can also provide a good place for them to grow. "Decomposed granite" is like any other mulch and will help keep "weed" growth under control for a time. Whether the expense is worth it is debatable.

kimmq is kimmsr

Weeds would grow eventually and then you'd have a nightmare time trying to take up the weedcloth.

I would recommend getting a stirrup hoe if you don't already have one and hoeing off all seedling weeds when you get a dry spell. (Don't hoe if it's going to rain. The seedlings will just reroot.) Do it when the weeds are tiny seedlings. Do it repeatedly and you will win.

A hoe is a fraction of the cost of the other stuff and it works.

Thank you to both of you!