I would defintley apply beneficial nemetodes for grub control (it is very effective) and corn gluten meal in the fall and spring to help reduce weeds. BE careful not to apply corn gluten meal if you are trying to germinate grass seed, as it prevents germination. I would also give your lawn 2-3 good waters a week as opposed to frequent watering.

Start by reading this topic:

http://www.dirtdoctor.com/forum/viewtopic.php?t=382

The St. Augustine will take over most of the weeds as you improve your soil. Probably one of the best things to do now is to lay down a thin layer of screened compost over your yard. Some molasses (liquid or dry) will also help to jump start things. In the fall apply Corn Gluten Meal (CGM) for fertilizer and Spring weed control. In early Spring apply more CGM for the summer weeds and to give your lawn a good start. I water at the most once a week, very deeply. I usually water after I mow, and pull weeds the following day. There is much more information in the Lawn Care Forum that would be helpful to you.

I hope this helps

There is a Lawns forum for questions like this. This forum is for making stuff at home to spray or spread in your garden.