Here is a link that might be useful: click for the Bermuda Bible here

I got news for you.

That ain't bermuda.

Sorry. Had phone call.
The first thing you want to do if you want to start over is to begin a applying roundup to your weeds, bahia and what remains of the st. augustine mix. (will take months of repeated applications on that stuff) Scalp it as low as you can go with your mower by removing the wheels of your mower if necessary to get down to half inch or 3/4". Then haul in some good top soil and level the lawn with 3/4" of top soil and re-SOD that area. Don't forget to water and fertilize your lawn and use pre-emergent at the appropriate times of year. Do not mix species of warm season grass. Pick one... bermuda, st. augustine or bahia. They are not compatible.

Is that sea grape I see? Are you within a mile of the coast?

Your back yard looks like it doubles as home plate. Do you have a lot of activity in the yard that we should know about? Dogs, for example?

Are you willing to water and mow the lawn weekly? Are you more willing to fertilize 0 times per year, 4 times per year or 9 times per year?

St Augustine will work for you but only if you are willing to water it once a week. If you are then start watering and put some fertilizer down. If you are not willing to do that, then bermuda is your only choice. If you are not willing to fertilize the bermuda, it will look a little weedy and thin. Of the two, bermuda requires more input to make it look nice. You can be very lazy with St Aug and it will look nice but you cannot let it go dry.