Most used car problems are not bad luck — they are things the buyer could have checked and did not. Work through these steps in order and you remove almost all of the risk.
Know the price before you look
Spend an hour comparing the same year, variant and kilometres across a few listing sites. You are looking for the realistic middle of the market, not the cheapest ad. Once you know that number, a car priced far below it becomes a warning sign rather than a bargain.
Run a PPSR check
The Personal Property Securities Register is the national government database. For a couple of dollars at ppsr.gov.au you can search a car's VIN and see whether there is finance owing, whether it has been reported stolen, and whether it has been recorded as written off. This is the single most important check you can do, because if a car still has money owing on it, the lender can repossess it from you even after you have paid the seller.
Read the service history
Ask for the logbook and invoices. You want to see regular servicing at sensible intervals, matching the odometer. Gaps of two or three years, or a jump in kilometres with no records in between, need explaining. A thick folder of receipts is worth real money.
Pay for an independent inspection
A pre-purchase inspection by a mechanic or motoring club costs a small fraction of the car and finds the things you cannot: worn suspension, oil leaks, previous panel repairs, tyres about to need replacing. If a seller will not allow one, walk away — that answer tells you everything.
Dealer or private?
Buying privately can be cheaper, but you get very little protection: the sale is essentially as-is. Buying from a licensed dealer costs a bit more but brings consumer guarantees under Australian Consumer Law, and in most states a statutory warranty on eligible used cars plus a cooling-off period. The rules differ between states, so check what applies where you are buying.
Be willing to walk
Never buy under pressure, never pay a deposit to "hold" a car you have not inspected, and never transfer money before you have seen the car and checked the seller matches the registration papers. There is always another car.