The problem with a lot of body care and cosmetic packaging is that while individual components may be recyclable, often different plastics are fused with metals and even glass to present you with the one beautiful product. Separating these can be a problem so if you have the opportunity to reuse containers or buy from a supplier who refills, it is a good idea to do so.
When shopping for body care products, make your buying decisions by paying forward. Base your decisions as much on what is in your product as what happens to your product packaging.
Be aware of microbeads (tiny plastic beads) in body care products as well and avoid them. Microbeads are typically designed to be abrasive so are found in products like scrubs, toothpastes and shower gels.