The domain registrar to choose depends on two things; price and ease.
To buy a .com.au domain name, Crazy Domains, Netregistry and Ziphosting are popular options.
To buy a .com domain name, you can use any of the above, otherwise GoDaddy and Name.com are popular choices.
Some people prefer to buy all their domains with the same registrar, even if they have to pay a little more per domain – just for the fact that then all their domains are in the one places.
Other people choose to, for example, buy their .com.au domain names through a service like Crazy Domains, and their .com domain names through a service like Name.com.
There’s no wrong answer – it’s whatever works best for you.
If you choose to buy different domain types through different companies, a helpful hint is to create a simple spreadsheet where you list the domain and the registrar it’s been registered and your login credentials. If you want to go a step further, add in the date when you’ve registered it and when it’s due for renewal (usually 12 months after the registration date).