I've about 5 inch of fairly stony soil then below it very rocky and
sandy.

My intention is to sift the soil and remove all the stones and lay
stones down first, then put the sifted soil top of that. Then grass.

I'm sifting with a garden sifter thingy and the size of the holes are
about 1cm square. Should I sift with a finer sieve?

I'm wanting a lawn bowling green-ish.