I would avoid layers if possible mate , i find they tend to make barriers in the heap !
I akways mix mowings as best as poss.
If you have a lot of hard stuff to compost , then you can add extra grass around that , but not too much .
Any of the daggings or strawy stable manure will mix well with the grass .
Any stable manure with sawdust compost in a separate heap ,it takes much longer to break down .
Pee is a perfect activator for the heap . Male pee tends to be better than female , but avoid using any if the person is on meds , especially the pill !
Any thick stuff like cabbage stalks , smash with a lump hammer first . Although any with club root just burn and use the ashes .