Serious "it depends" questions. If the weeds are winter annuals, use Weed-b-Gone through a hose-end sprayer on the bermuda. It is really tough and will take about anything you can throw at it. Fertilize with a good quality fertilizer (not CO-OP brand) such as Scott's or Bayer in a few weeks, then again at the start of June, and once more in the fall. My other (and favorite) choice is to hit it with a quality organic like Texas T, Medina Pelleted, Gardenville Soil food, etc ..... now (since you don;t know the history from last fall). Use the same schedule the first year as above.
Augustine is tough to deal witgh when it comes to weeds. Way too many of the over the top sprays end up either not working, or smoking the augustine at the same time as the weeds. This is one of the absolute few times I will ever recommend weed-n-feed products for the start up of a long term program on Augustine. Use it if you must, but keep it out of your flower beds and away from your shrubs. Use it the one time in the spring, then switch to something else (above) later in the year. From now on, spot treat or use a pre-emerge like Balan in the early fall and early spring until you have the weeds to a minimum.
