This pic is prior to me spreading the seed. i did two passes. From the start of the concrete slab to the fence line is what im starting with. Everything before the slab is what im dealing with

Im new to the lawn game. Im located in Jacksonville, Florida. New to North Florida from South Florida so its a whole new animal. Im use to lawns staying green year round. We were dealt a bad hand at the house were renting and im now trying fix the backyard grass for my toddler and dog so they can play in something decent. I just put down some tall fescue seedlings after dethatching and scarifying the half of the yard that im starting with. Whats the best thing i can put down to help the germinating process? A turf/seed starting fertilizer? A manure/ compost soil? or both?