The common properties of PVC vary wildly with the concentrations of plasticizers and filling reinforcement.
The common properties of PU vary wildly with the choice of isocyanate and cross-link density. PU comes in foams, fibers and hard plastics.
Modifications, copolymers and alloy blends are common with both.
When selecting a plastic, it is useful to gather requirements rather than emulate another plastic.
Some physical properties to look into are: Glass transition, melting/vicat softening point, degradation onset temperature, thermoset/thermoplastic, solvent resistance, transparency, UV-resistance, food/medical-safety, tensile strength and Young's modulus.
With regards to manufacturing some properties to look into are: pot life, working time, tack time, demold time, cure time, cost at scale, shipping and sourcing.
With regards to your question you're also considering if they are biobased(ASTM D6866), their recyclability and their compostability.
The only bioplastic that is highly recycled is HDPE. The only other plastic that is highly recycled is PET. There are probably more recycling operations for other plastics, but they are much smaller in scope.
Compostibility is dominated by starch and cellulose plastics.
As a start, you should visit Matweb for the basic properties of various plastics.