my poorly garden

hi, this is my first post so please be gentle! after a number of years i have decided to repair my so called lawn. about 2 weeks ago i put a load of evergreen 4 in 1 on the grass in the hope that it would remove all the weeds etc. being a novice at all this i just wondered if someone can give me some advice on what to do next. i am just wanting a low maintenance grass for the kids to play on so nothing special, and im not looking for a quick fix however it is heavily shaded by the house. on taking the photos today i noticed that i have got mushrooms. i dont recall seeing them before.it is my intention to scrape all the moss up but do i re-seed or will the evergreen feed the grass enough for it to eventually grow out over the old moss site? any suggestions welcome.