Round up, or gramoxone (Paraquat) will burn all of the weeds down, but they will come back. You will have to weed the garden throughout the year. There are some chemicals that have a residual affect, but you have to be careful. You don't want to put a chemical down that will damage what you plant. In the fall, after you have harvested your garden you can spray a round up atrazine mix on it. The round up should kill most weeds that are up, and the atrazine will prevent ANYTHING from growing for 90 days. Including anything planted within that 90 days. Again you have to be careful. It's difficult to give advice on what to spray without knowing what kind of weeds you have.