Paging Yard Gurus

Recently purchased a new house and the back yard grass needs some work. The front yard has some good st. augustine grass with the occasional spot of clovers and other weeds. I just used a normal weed and feed for the font yard. Will this be fine for the front or are there better options?

However, the back yards is what i call trash grass. It is mostly weeds with the occasional spot of st. augustine. There are also some spots that don't really have any grass and its just dead spots of grass or dirt. What is my best option for the back yard? Should i just till up the entire back yard about a 1/4 of an acre maybe a bit smaller and relay sod? Or is there a seed i can spread that will help grow grass and kill the weeds?

TIA, don't know much about grass and doctoring it up.