Regarding the car purchase stuff, not sure if you are looking for brand new or what. I got mine second hand from just a private seller (dude selling his car). It was super straight forward, he had the pink slip for the car (ownership) and had whatever (cant remember as this was like 3 years ago) transfer documents were required already signed ahead of time. So once I had all that I basically just had to take it to the DMV the next day to get it transferred into my name, then got it insured and good to go. When getting your insurance they'll want your aus driving history as well since itll impact the cost if theres any at fault stuff etc, this cost me like $26 or something from the department of transport in QLD, was online and instant.
Main issue I guess is since we arent familiar with the documentation you are just putting a bit of faith in the other person that's selling it, so best to just do some research on what the documents you need from them are. I did the research back then before getting mine (but again it was 3 years ago so dont remember the exact documents).
Theres a few other steps that vary state to state, in California your car has to pass a smog test before it can be registered as well. The previous owner is supposed to do this before selling it (mine didnt, so I had to get this done, was another $35-50 or so).
List of what you need (in CA as an example) -
https://www.dmv.ca.gov/portal/vehic...ing-a-vehicle-purchased-from-a-private-party/