Seems to me you're more likely to get a green woodpecker in your garden than the other two.
That's the place to see one.
If you want to maximise your chances, get a medium sized log, drill a load of holes in it and stuff mealworms and stuff in the holes then hang it vertical in the garden somewhere.
( baldmonkey a frothy foul-smelling vaginal discharge, Thu 3 May 2012, 11:47, archived)

there are some dead trees up the road, I heard one drilling there a while ago
I think it was a greater spotted, it was pretty big
( spangolin - the odds are good but the goods are odd, Thu 3 May 2012, 12:00, archived)