I agree with Goldwing.
The words “reliable” and “under $4k” are rarely heard in the same sentence.
The problem with used cars is that the second, or third, or fourth owner is at the mercy of the previous owner(s) who may not have maintained the car properly. I can tell you that, based on a many posts in this forum, there are apparently a lot of people who do not maintain their cars properly. The first owner will rarely suffer, but subsequent owners will pay the price–both literally and figuratively.
All I can suggest is to buy a copy of the Consumer Reports Used Car Buyers Guide in order to see the attributes of everything that is out there in the US marketplace–including historical reliability data. The guide also includes lists of recommended makes and models in every price category.
Once you have narrowed down the makes and models that appeal to you, then you can begin shopping. Although this will make your quest harder, you should only consider vehicles that come with maintenance records. This will limit your selection, but you will be left with vehicles whose maintenance you can verify, and that is vitally important. Then, once you believe that you have found a viable candidate for purchase, pay your mechanic to do a pre-purchase inspection.
None of this will guarantee a reliable vehicle, simply because your preferred price range means that you will be looking at vehicles that are at least 8 to 10 years old, and a vehicle of that age will break down on occasion no matter how well it has been maintained. But, if you follow my advice, you will greatly improve your odds of finding a decent vehicle.