Mazda 2 2013 Problems

You've chosen a good brand in Mazda, and good models in the 2 and 3. Both are good cars and give little trouble, so you can't go far wrong with either one. There are other brands as well, but I would recommend that you stick with Japanese brands and not be tempted by European cars, which can be expensive to service and repair. Look for a car in good condition and well presented both inside and out, a car that drives smoothly, and doesn't have any odd noises or vibrations. Don't take any notice of the salesmen trying to sell you a car; they're just trying to relieve you of your money and some will tell you anything to make that happen. If you can't take a trusted friend along to help you assess a car, consider getting the NRMA to check it for you.

Skipping oil changes is the worst possible thing to do, the oil will get thick and sludgy and the risk is that it will block the galleries in the engine, and in the worst case it could cause the engine to fail.

If it were my daughter I would be looking for safety and reliability as top priorities in a first car. With your budget I would be looking at a 2013/14 Mazda2, a 2014/15 Kia Rio, and a 2014 Toyota Yaris.