I would say the most important things are to listen to the sound of the engine from the whole duration between cold start and operating temperature, and to check the body for rust very carefully. The body and the engine can cause the most expensive problems. If you have never owned a car before, you probably do not have the ability to detect potential issues from the engine sound.
Apart from that, take it to a test drive and test that all gears work well and that there are no problem indicator lights on the dashboard. However, if you have little driving experience, you won't gain much from the test drive. Check also the service history of the car.
It should be mentioned that expensive problems can be hidden by quick and dirty fixes, so if the seller is trying to screw you, chances are you won't notice it. I once purchased a second hand car where the engine was poorly designed and had noticeable piston slap even when hot only after 80 000 km. The seller had masked the sound by pouring oil from the spark plug holes. Turns out it was a very expensive mistake and I scrapped the car 3000 km after buying it. It could probably have been driven, I just couldn't tolerate the sound. I no longer buy second hand cars for this reason (and I no longer buy Volkswagens).
Another thing you can ask yourself is to assemble a list of common problems of the model of car you're planning to purchase, and then ask how to detect the problems in the list. If you have no idea how to detect those issues, then don't buy a second hand car!
The general rule of thumb is if it works, don't fix it! Thus, you can expect that most second hand cars have at least some kinds of problems. I would prefer one-owner cars and specifically those where the owner had a clear reason for purchasing a new car, e.g. due to needing a larger car. Thus, a small second hand car can be a good purchase (the owner probably needed a larger car due to e.g. increased family size), but a large second hand car probably is not a good purchase (why would the owner sell it if it works perfectly? Even a divorce isn't good reason for replacing a large car with a small one due to the high transaction costs of trading cars).
You should also note that because small cars are cheaper than large cars when new, if you have a fixed budget, then purchasing a small car means you have the money for a newer car that probably has less issues. So, to save money, the correct choice is to purchase as small car as possible and drive it until it needs to be scrapped. Note also that car models tend to increase in size every year and increase in fuel efficiency every year.
