Differentiable Microstructure Characterization and Reconstruction (DMCR) is a recently-proposed and efficient microstructure reconstruction algorithm with great versatility regarding the prescribed microstructure descriptor. To fully exploit this versatility, the present contribution provides an in-depth analysis of the suitability of various established and novel descriptors. As a first step, new differentiable descriptors are introduced. Some of these are differentiable approximations to well-known descriptors like the lineal-path function, while others are inspired from feature engineering and are new to the materials science community. As a second step, these descriptors and their combinations are compared regarding their dimensionality, sufficiency for reconstruction, computational cost and influence on the convergence rate of the reconstruction process. Finally, a conclusion is drawn to assess which descriptors are best-suited for which microstructure reconstruction task.