I favour letting the student initially fly the circuit and landings with no checklist items at all. Most flying schools insist on a ridiculous amount of unnecessary drills which only serve to daze the poor student and he spends most of his circuit trying to remember drills and never gets around to flying the aeroplane.
Later when he gets the hang of flying the circuit reasonably well, then you can teach him the important checks. Anything more than is recommended in the manufacturer's POH is usually too much.
I am sure that the secret to early solo is a reduction of checks to that necessary for safety. The Before Landing checks in a Boeing 767 are far less than those taught at some flying schools for a Cessna 150.