Right now weeds aren't really a problem (we've got a foot of snow on the ground) but during the grow season I put landscape fabic around any plants I put in the ground. As benny said newspappers work as well. As far as the organic matter, it's probably just personal perception but I don't like anything that is still in the early stages of the composting process under my plants. Any water that may splash at the base of your plants, weather it be from rain or garden hose, can tranfer nasty deseases to your plants (this is was causes alot of Tomato blight).
It's just my opinion but the fastest, easiest, and surest way to stop them dead is remove all the weeds,( I like a stirrup hoe ), lay down the landscape fabric ( pin it down good using pieces of wire clothes hangers cut to about 8 in. and bent in half), and viola done. Water can go through the landscape fabric but won't splash anything but water on your plants.
Best of luck, take care.