You can get more complicated but your results won't be much better. Here we go

Water deeply and infrequently. More on this later. I realize you live in FL where everyone wants to water shallow and frequently, but you will really do yourself a favor by deep and infrequent watering.

Mulch mow every week or 2 (or 3) at your mower's highest setting. Preferably mow the day before you water. If you have one of the newer hybrid St Augustines, you may need a new mower. They are pretty dense in the full sun.

Fertilize with organic fertilizer every time to keep your soil's organic matter going. With your soil you need it every time. I would recommend using alfalfa pellets (rabbit chow) from the local feed store. If the cost is more than $15 for 50 pounds, let me know and I'll have other suggestions. The application rate is 15-20 pounds per 1,000 square feet. Apply on Washington's Birthday, Memorial Day, 4th of July, Labor Day, and Thanksgiving. Organic fertilizers take 3 weeks to see the effect, but if you follow this schedule, then you should not really see an effect, because the lawn will just be green all the time.

Spot spray weeds with an atrazine product in mid April and after the summer heat breaks. Second app is only if you need it. Don't expect immediate results. It takes 3 weeks and "suddenly" the weeds are gone. Herbicide sprays are foliar mists, not soil drenches.

Watering: Deep and infrequent is the mantra for watering. This is for all turf grass all over the place. Deep means 1 inch all at one time. Put some cat food or tuna cans around the yard, and time how long it takes your sprinkler(s) to fill all the cans. Memorize that time. That will be the time you water from now on. My hose, sprinkler and water pressure takes 8 full hours to fill the cans. Your time will likely be less. I like gentle watering. As for watering frequency, that depends on the daytime air temperature. With temps in the 90s, deep water once per week. With temps in the 80s, deep water once every 2 weeks. With temps in the 70s, deep water once every 3 weeks. With temps below 70, deep water once a month. Note that you have to keep up with quickly changing temps in the spring and fall. This deep and infrequent schedule works in Phoenix and in Vermont, so it should work for you. The reason for deep and infrequent is to grow deeper, more drought resistant roots and to allow the soil to dry completely at the surface for several days before watering again. If it rains, reset your calendar to account for the rainfall.