New House Weed Control North Florida

I am working on a plan for our new yard. We live in the Florida panhandle and our yard needs a lot of work, it is a mix of St.Augustine and Bermuda, maybe some Bahia. Mostly weeds though unfortunately. I think we missed the pre-emergent window as the soil temps are in the mid 70's.

I am thinking this year should focus on enriching the soil and trying to get rid of as many weeds as possible. Hopefully next year we can sod some Zoysia or St. Augustine.

I have been watching the lawn care nut for many years and am leaning to supporting them some and buying some Flagship fertilizer, and some Image post emergent.

My questions are should I add something else to this for more nutrition? Can I use them at the same time? I just got a new earthway spreader that I am dying to break in. One worry I have is spraying too much post-emergent because there are a TON of weeds.

Any advice is greatly appreciated.