The correct order of NAT priorities is Static NAT, IP pool NAT, and hide NAT. Static NAT is prioritized first because it provides a one-to-one mapping between internal and external IP addresses, ensuring consistent address translation. IP pool NAT is next as it involves a range of IP addresses to handle the translation, generally used for outbound connections from an internal pool. Hide NAT is prioritized last because it translates multiple internal addresses to a single or limited set of external addresses, often for outgoing traffic, and is used to 'hide' several internal devices behind one external address.