What's the pricepoint at which buying a less expensive car becomes not worth it?

Obviously brand new cars have the least amount of mechanical issues, but the beaters you get for $1000 have so many problems you can end up sinking more money than the car is worth into repairs and end up needing to junk it every time a major issue comes up. Somewhere between those two extremes there's a point at which you're minimizing the cost of buying the car, but not so much so that you'll pay for it in repairs down the road and with the vehicle being unreliable.

I'm asking this because I like buying my cars outright to avoid loans and would like a savings goal. My current car I bought for $6,000 cash and it had just under 100,000 miles at the time and it's had only one or two issues that cost more than a few hundred dollars, so I think that's a pretty good deal.