Geometry
Cylinder
The Geiger counter is designed as a cylindrical shell, functioning as a cathode with a thin straight wire through the center that functions as an anode. The cathode is negatively charged and the anode is positively charged. There is an electric field being emitted radially outward from the positively charged anode. Any positively charged particles that interact with the Geiger counter will be drawn out towards the cathode. Particles like muons will be attracted to the anode wire.
Sphere
A sphere is a perfect equipotential surface. But since the Geiger Counter is an electrode there has to be a cathode part and and anode part. The spherical shell of this theoretical counter could have to have an anode part in the center. There would also have to be a wire running from the anode out trough the sphere. This would compromise the symmetry.
Therefore, the cylindrical shape of a Geiger counter is the most effective geometry because of its an equipotential surface.