Definitely 3. Definitely any combination selectable. Almost certainly two coils per pickup, with a 5 way switch for none/coil 1/coil 2/serial/parallel (per pickup).
You want
three 5-way switches, one for
each pickup? Well, if you wanted all that "switchability", you'd definitely need humbuckers. Single-coils are just, well, single coils. I'm not sure all the options you want there are possible; maybe with rotary switches (like PRS use), although I don't really know much about how those work.
The problem with really complex wiring is you may have 57 different options but probably only 5 or 6 of them will be really distinct and useable. And it's confusing! The Jimmy Page Les Paul has dozens of sounds, but you might have to operate
four push-pull pots just to get from one sound to another.
On the other hand, if you go with single-coils, you can combine them with each other in interesting ways. Maybe you could get 3 P-90s and copy one of those Strat wiring schemes that let you get all the different combinations of the 3 pickups, in series and in parallel. Or perhaps you could do something like the PRS 513, which uses 5 single-coils and 2 switches to give 13 different sounds.
