Proprietary (Private) Company
A proprietary company must have at least 1 director. That director must ordinarily reside in Australia. If you're just starting out and looking to open a Company, a Proprietary company is most likely the suitable structure for you.
A public company must have at least 3 directors (not counting alternate directors). At least 2 directors must ordinarily reside in Australia.
Source: Corporations Act (2001)