I'd like to start over with growing lawn and some plants on a small patch of garden (20-25 m2 at most). I removed the weeds/existing grass from the top by digging through it and noticed that the topsoil is a bit of a mess. There's some construction site rubble (small pieces of bricks/cement) and all kinds of things that don't belong there (pieces of plastic foil, shards, etc).
I understand that lawn may not be too needy in terms of soil quality, but I thought I'd try to improve its quality anyway; also to grow a few other plants such as vegetables and flowers. I could clean up the soil (sift? and remove obvious rubbish) and enrich it by adding mulch, or, alternatively, remove the whole topsoil and get completely new one?
My question is what are common ways to go about preparing such kind of soil for growing lawn (should I remove it entirely)?