A new burning plasma systems code has been developed for analysis of a next step compact burning plasma experiment with copper-alloy magnet technology. Two classes of configurations are considered: type A, with the toroidal field (TF) coils and ohmic heating (OH) coils unlinked, and type B, with the TF and OH coils linked. Curves of the minimizing major radius as a function of aspect ratio R(A) are obtained for each configuration type for typical parameters. These curves represent, to first order, cost-minimizing curves. The type B curves always lie below the type A curves for the same physics parameters, indicating that they lead to a more compact design. However, the fact that the type A OH and TF magnets are not linked presents fewer engineering challenges and should lead to a more reliable design. Both the type A and type B curves have a minimum in major radius R at a minimizing aspect ratio A typically above 2.8 and at high values of magnetic field B above 10 T. The minimizing A occurs at larger values for longer pulse and higher performance devices. The larger A and higher B design points also have the feature that the ratio of the discharge time to the current redistribution time is largest so that steady-state operation can be more realistically prototyped. A sensitivity study is presented for the baseline type A configuration showing the dependence of the results on the parameters held fixed for the minimization study.