Semi-crystalline polyolefins PP and HD-PE are often used for storage boxes, trash-bins, and buckets. They look and feel very similar.
PP is available as a homopolymer and copolymer. The latter has lower strength and modulus but is more impact resistant.
If stiffness is not an important factor, LD-PE might be an option.
Rigid PVC is one of the most used plastics in the world. It is widely used in the construction industry. It includes chlorine which makes it problematic to produce. PVC is not a particularly relevant choice of material for consumer goods.