Answer: The newer non-organic mulches are attractive, and if applied thickly enough, do a good job in suppressing weeds. They are permanent, however, so if you ever change your mind about the color, or even about having it in your garden, you'll need to rake it all out and dispose of it. For this reason, I'll recommend laying weed barrier down on the soil before adding non-organic mulches.
Since you asked my opinion, I'll vote for using organic mulches rather than non-organic materials. Yes, organic mulches break down and need to be refreshed or replaced every few years, but as they are breaking down they are providing nutrients to the soil. And, when they need to be replaced, all you need to do is dig them into the soil. They enrich the soil and after a few years of digging organic mulches into your garden beds you'll eventually have rich, loamy soil - much to the delight of your plants.
Any material, organic or not, will suppress weeds, slow water evaporation and help moderate soil temperatures. The key is in digging out the weeds prior to placement, and making sure the mulch is about 3" thick.
Any groundcover that grows thick enough to shade the soil surface will help suppress weeds. Pachysandra, ajuga, vinca minor, or even wooly thyme are all good weed-suppressing groundcovers.
Best wishes with your garden!
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