Re-levelling a lawn

We have a simple lawn with beds around the outside (approx 75m2)

The lawn slopes away from house (approx 1 in 18) and is quite bumpy - worsened by some recent building work which has wrecked the lawn and bits of stone and brick everywhere.  There is some topsoil in place, but underneath is heavy clay, some of which has been brought to the surface when a soakaway was put in for our extension.

I plan to remove the old lawn and grade it to about 1 in 50 using ??? (see below).  I was then going to lay about 3 - 4 inches of good quality screened topsoil and then turf it.

I plan to use a rotavator / tiller to blend the old and new soils, but my main question is should I use screened or unscreened topsoil to level the sub-surface out? I have seen an argument that unscreened (as well as being cheaper) would help with drainage and prevent bad settlement.  However, another part of me thinks that screened and a real effort to remove all stones would be a better job?

If I used unscreened to fix the levels, how much screened to lay on top (The bottom end of the garden needs to come up about 8 inches in total)

Any tips?

Your advice much appreciated.