I'll second Attrill. I've avoided chemical weed control in my food bed, and have managed pretty good control with fire, mulch, and modest tillage.
If you had more time, a good way to sterilize the soil without fire is to place black plastic over damp soil, and let the heat buildup from solar heat cook and kill seeds left in the earth. If you have the space, lay down strips of black plastic between your plantings. At the end of the season, reserve some time to cover all w. plastic, and let the last warmth cook the garden. Then rake in autumn leaves and let rot over winter.