Horseshoe Magnet geomotry/strength

Does anyone know is there is a rule of thumb for making a really strong efficient horseshoe electromagnet? Like width of leg vs total height of horseshoe or something of that nature? Will making it taller with more windings make it more or less efficient? That sort of thing. Thanks.

Or here is an easier question, what is the best geometry for creating the most efficient electromagnet?

There will be a limit to the strengh of magnetic flux that can be contained with a core of any particular cross section. That limit depends on material.

So a core with a larger cross section can carry a stronger magnetic field. You should google of wiki for "principles of solenoid design" etc, it's a bit of a lost art these days as very few people design and build their own solenoids.