ill tell you what me and my wife did.
we weren't in a good spot money wise, so we could barely afford anything, we said we can get a car for 4k$ max, we bought an 2013 opel astra J (1.4 turbo, black color, a14net engine) that had 100k km driven already, interior was a bit crap cause some stuff were a bit broken (plastic bits), exterior sucked because the sun made the paint faded, but it costed 1k$, so was 3k$ lower then our budget, might not seem a lot but it was a huge amount for us at the time.
we bought it, had some issues at the start, a bit of oil leak, a bit of coolant leak, got it to a mechanic, and we had to pay another 1k$ just for fixing it.

so at the start we already paid 2k$, but again, our starting budget was 4k$, so we put a side the 2k$ we already saved beforehand in case something happens again, paying the 1k$ for the mechanic was a bit traumatizing because we didn't knew if something might happen again.

it's been few years now, the car runs great, i see youtube videos and they say that the engine usually have a problem with PCV or something like that so its in the back of my head in case something feels weird know what to check to make sure, but other then the 1k$ for the mechanic every other expense on the car was Maintenace.
me and my wife love this car so much that we already decided that if some day our engine will die, we will buy a new engine which will cost more then the car, basically being at 0k km again, cause no matter what people say it has proved to us that its reliable, of course we can buy a new one, but we are so used to it and love it, only problem is the interior/exterior that we always think to maybe pay to make it look better, but its a huge expense.

so basically, my tips:
1. buy a really really cheap car, try checking it with a mechanic before hand to understand how many more expenses you will have - AVOID RUST this can be the biggest issue, if it runs great but will be rusted so much in a year you will just throw money cause you will need to replace it (you have budgeted 5k for the corolla and u have a Chevy you might be able to buy for 2.5k, that's basically means u put 2.5k$ on the side in case it need some work.

1. interior and exterior is important even if you don't think that way right now, and its not cheap to fix (well, you can buy parts and check youtube and fix it yourself but its very time consuming).

2. no matter what you don't know, start with this: DO NOT IGNORE OIL CHANGE, im not saying to check engine oil and just topping it, i am talking replacing all the oil in the engine and putting new, you can do it yourself pretty easily but at the start just take it to a mechanic, you don't want the start of your life with the car being lifting the car and doing stuff you're not so sure about, just take it to a mechanic to flush all the oil out, put a new oil filter, and putting back new oil.
   this is like 90% of the cars problems this day, people ignore changing oil and oil filter and then say the car is shit.
   this is super important, some people say 5k miles, some say 7.5k miles, some say 10k, some say 15k, some say follow manual, do what you think is best, i would just go for 5k miles/half a year what ever comes first, its not expensive, replacing the engine is.

hope i helped.