A lot of things influence my decisions:
-Price is always a big factor. I think it is for almost anyone who can't afford to throw hundred dollar bills in the river just for fun.
-Mileage. Although higher miles doesn't scare me, I always prefer to see if I can find a good deal on a lower mileage car. That way I know there's a lower chance of me having to fix anything as soon.
-Exterior condition. I know how to paint and I love to paint, but if I look at a car with most panels in dire need of repainting, I expect to be getting a very good deal on the car. Painting a car is expensive if you can't do it yourself and very time consuming if you do it yourself.
-Mechanical condition. I always test drive a car before I buy it. If someone says they won't allow test drives, I'll go buy a car from someone else. Plain and simple, I need to know I'm not going to lose a wheel or blow the motor as soon as I start to head home. I like to know what's wrong with it so I know what kind of work I'm going to have to put into the car.
-Has it been smoked in? If I can tell a car has been smoked in a lot, I won't buy it. I hate smelling like smoke and I hate the smell of smoke. The only way I've found to completely get rid of the smell in a car is to replace the entire interior. I won't buy a car that needs the entire interior replaced unless I'm getting the car dirt cheap and most people won't let a car go like that just because they smoked in it (which is a common activity to them).
-Sales people. Seriously, the people trying to sell me a car influence whether or not I buy. If they push really hard to get me to buy the car, I'll probably walk away unless I absolutely love the car. I like people who are going to be real, tell me what's wrong with the car, let me look it over, and work with me to get a fair deal on both ends.
And there's plenty of other factors that influence my decisions, but I'm very picky with cars.
I do have to say though, safety is not one thing I look at. Thanks to Bedbugabscond for mentioning it. It's never been something I cared about. As long as it meets all my personal criteria, I couldn't care less about how safe a vehicle is compared to other vehicles.