What are the minimum requirements for setting up a Hong kong private company?

Anybody can form a Hong Kong company. However, a Hong Kong company must have at least one director (individual), one shareholder (individual or corporate), one secretary, and a registered office address in Hong Kong (post office box is not allowed). ONE IBC will provide a registered office address and secretarial services so that you can serve as the director of the company. ONE IBC can also provide individual Nominee Director and individual Nominee Shareholder if needed to protect your privacy.
There is no prescribed minimum share capital. For practical purposes, this is not usually less than HK$ 10,000 or the equivalent in a foreign currency. There is a capital duty of 0.1% payable on the authorised share capital (subject to a cap of HK$ 30,000).
And the minimum requirement to form a private limited company is one shareholder/director who can be the same person.