In the successful transition towards a circular materials economy, the implementation of biobased and biodegradable plastics is a major prerequisite. To prevent the accumulation of plastic material in the open environment, plastic products should be both recyclable and biodegradable. Research and development actions in the past few decades have led to the commercial availability of a number of polymers that fulfil both end-of-life routes. However, these biobased and biodegradable polymers typically have mechanical properties that are not on par with the non-biodegradable plastic products they intend to replace. This can be improved using particulate mineral fillers such as talc, calcium carbonate, kaolin, and mica. This study shows that composites thereof with polybutylene succinate (PBS), polyhydroxybutyrate-hexanoate (PHBH), polybutylene succinate adipate (PBSA), and polybutylene adipate terephthalate (PBAT) as matrix polymers result in plastic materials with mechanical properties ranging from tough elastic towards strong and rigid. It is demonstrated that the balance between the Young’s modulus and the impact resistance for this set of polymer composites is subtle, but a select number of investigated compositions yield a combination of industrially relevant mechanical characteristics. Finally, it is shown that the inclusion of mineral fillers into biodegradable polymers does not negate the microbial disintegration of these polymers, although the nature of the filler does affect the biodegradation rate of the matrix polymer.