Depends on where you’re going

In Victoria you need to purchase a myki card to use trains, trams and buses.  

In New South Wales, you can purchase paper tickets every day you wish to use public transport. Or an Opal card

In Queensland you need to purchase a Go Card.

There are other options in the other states and territories, and you need to be aware that the contactless payment cards are only valid in the state or territory of purchase. 

everything you need to know you can find in here

https://translink.com.au/

Beware any " advice " from Tento.  Tento is a foreigner. 

https://allianzassistancehealth.com.au/en/living-i...

https://www.australian-trains.com/

i would contact places in australia and ask them about it

Believe it or not trains can be full. It is prudent to book in advance.

You can buy tickets one at a time if you want. There is no guarantee there is a seat for you on every possible train.

Do we get to pick a return train? Yes you can pick from the trains with available seats.

 How soon should we arrive at the station before our train leaves?

Arriving at the front door not quite the same as at the platform ready to board.

30 minutes to an hour should give you enough time to get to your train loading place. Obviously the small town stations are a little faster to negotiate than the main terminals.

Should we buy bus passes? Not a bad idea for your local travel saves on shoe leather and time.

You do know there are these PEOPLE called travel agents they can assist you with this.

Australia is very large there is a big difference with the long distance trains that run a few times each week and the network of trains near the big cities that have trains many times per day.

Bus Pass??  The local networks offer daily and multi day passes for unlimited rides on their networks of buses trams subways and commuter trains. A very good thing to make use of.

For city to city travel it depends how much you wish to ride if it is worth a pass.

This site can get you started.

https://www.railmaps.com.au/

Travel Agents make their living helping people arrange their travel. You are paying for their expertise and local knowledge .  Of course you can do it yourself for Free your time does not cost as you search out the deals and packages.

As you have not asked about places to sleep Do you assume every place has a room waiting for your use?

Have you considered how you will get from sleeping place to train station?

Maybe a special event during that time? A night of theatre or music a sporting event. Tickets can sell out months in advance.

Travel Agents can arrange a package of things for you. You can have detailed hour by hour plan of your time or something more flexible.

Travel Agents have access to package deals you will not find online.

It is prudent to have booked before you travel your first and last nights sleeping place. You have enough to do upon arrival and departure no need to add find a place to sleep NOW to your day.

So what trains are we talking about here?  Are you looking at Sydney's trains, part of their public transport system?  The Ghan?  The Overland?  Australia doesn't have a big train network.  Are you a train tragic?  You probably need to do some research on what it is you want from your Australian train experience.

Instead of going to Australia you should donate