Actually you need a Star Track account to send anything with them and the minimum required spend is in the thousands of dollars a month. They were going to expand Star Track to the general public but that never happened. Australia Post only relationship to Star Track from a delivery point of view is Post Offices operate as a pickup location for undelivered Star Track items, you don't send Star Track items from Australia Post. Though some Australia Post contractors have both a licence for Australia Post and Star Track. Outside of that they operate as two separate companies despite both being owned by Australia Post.

I don't know of any requirements to use Toll or TNT and I've never had an issue with them.

Stay away from Fast Way, they are slow and careless.