Coil Geometry Effects: and B Field Software

I'm in need of a simple magnetometer---and for lack of a Hall Effect sensor or money, it needs to be a spinning magnetometer.

I'm trying to figure out the advantages of different coil shapes. So far, I noted round coils are the easiest to calculate for. Square coils are said to give the better range. How about other polygons? To be honest, I'll probably go with the square coils no matter what, but I could really use the information.



Finally, does anyone have any experiences with free magnetic field software? I tried one called QuickField a while ago, but never really did anything with it.