I am developing a cosmetics line and have come up with a unique packaging design. It's not just the look, the package actually opens in a different way. Would I need a design patent or utility patent.
The answer is maybe both. Design patents cover the ornamental design of functional objects. If you want to protect the look of the packaging then a design patent is a good way of doing it. Utility patents cover the function of the design. If your package actually works in a way distinct and new compared to previous designs, it may be able to get a utility patent. The patented functionality must be novel and non-obvious not just over cosmetic packages, but possibly other types of packages also.
In general, design patents are easier and cheaper to obtain but perhaps easier to circumvent. In any case, I would strongly suggest you discuss this with a patent attorney or agent. Since you can't disclose your idea publicly, you can't get definitive answers from Q and A sites like this.
It's probably faster, much easier and cheaper to get US design patent granted than US utility patent. Depending on your resources you may apply for both, design and utility patent. But design patent application may be sufficient.
But before making your decision you should always discuss it with patent attorney.
I would file for the design patent which as stated is much easier and cheaper to get, then file a utility provisional application (which is also cheap and easy & would at least allow you say you have a utility patent pending which you can abandon later or convert to a regular app if there is something patentable based on its functionality).
Unless there is some surprising or unexpected benefit, seems like it would be tough to overcome obviousness for the utility patent based on what you described.