Resolving the microstructure of heterogeneous materials has become indispensable for understanding and improving their bulk behavior. Any such analysis requires a faithful and controllable representation of the underlying microstructure. Virtual structures are frequently reconstructed from image data, which typically provide highly accurate geometries without a priori idealization and are therefore well suited for analysis, but less so for design due to their static nature. In contrast, synthetic structure generators enable parametric studies, yet many existing approaches are limited to matching coarse indicators only and disregard topology or higher-order geometric descriptors such as surface-to-volume ratio, aspect-ratio, or tortuosity. This contribution presents a unified framework for the microstructure generation of random composites with highly diverse morphologies. Building on our previous microstructure-resolved studies on filled rubbers, fibrous paper networks, asphalt mixtures, and fiber-reinforced polymers, we extend the approach to metals and metal-matrix composites. The goal is to generalize the underlying geometric modeling concepts into a flexible, extensible generator capable of producing both periodic and random representative volume elements. The core idea is to encode material-specific morphology through extended geometric descriptors while sharing common packing and topology-generation backends. For particulate systems, inclusions were represented by aspect-ratio distributions, measures of shape irregularity, interfacial transition zones, and inter-particle metrics calibrated against experimental imaging. For fibrous systems, directional distributions, fiber curvature, and connectivity statistics were incorporated to reproduce anisotropic networks and load-bearing paths observed in experiments. Different packing algorithms were implemented within the same framework, including sequential addition schemes and more advanced dense-packing and compaction algorithms. The generator was designed to interface with standard finite element workflows through mesh-oriented export formats and supports periodicity constraints required for computational homogenization. The resulting platform is intended to enhance reproducibility and comparability across material classes by providing a consistent means of generating statistically equivalent microstructures for parameter studies, uncertainty quantification, and data-driven multiscale modeling.