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

The minimum requirements are:
(1) At least one individual or corporate shareholder
(2) At least one individual or corporate director
(3) A company secretary
(4) A registered office address in Hong Kong (post office box not allowed)
(5) Auditors
(6) A Business Registration Certificate

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).