The round coil is conventient for production and symetry, so it is the obvious choice. To ease on heat transfer the coil is reltively thin (often just 1 layer or wire). The magent is formed to produce a relatiely homogenous and strong magentic flied at the coil. As an alternative form one could have a relatively long coild that extends beyound the magentic field, so that all the field goes through the coild - this way also gives a linear response (constant force for a given current independent from the position). This is a radial field to have an axial force from the current through the coil.
To get the flux to the inside it needs a cetain size inside, so that the coil diameter can not be very small. Some suitable steel plate are usially used to concentrate the magentic flied from the relaticely large area magents at the outside (at least for the classic form with ferrite magents). Often the magent itself is just on the outside with axial magnetization.