If you have a serious business, you should not opt for a free website. You need your own independent domain name. You should buy a domain name that is short, precise, interesting, catchy, and easy to remember.
Opting for a free sub-domain on a platform like WordPress or Blogger is a bad decision. With a sub-domain, you will have little freedom. With your own domain, you can create unlimited sub-domains and unlimited email addresses that end with your web address. You will also have access to the source code and you can change it anytime.
After buying a good Australian domain name, you will need to host it using web hosting in Australia. In most cases, you will purchase the domain name and the website hosting package from the same company. You need a superior hosting package if you want your website to handle heavy traffic and store many files.