For 4 grand you can buy MANY DIFFERENT CARS. Not just a Civic or a Cavalier. You can pick up a 90's model Dodge Stealth for less than that. They are sister cars to the 3000gt by Mitsubishi and much like the Civic, their parts in abundance. You can also easily find a mid-90's Buick Roadmaster, Chevrolet Caprice Classic, or Oldsmobile Classic with a V8.
They get anywhere between 18-28 mpg, are four doors, and the 94-96 models have the extremely reliable (less Optispark) LT1 motor. My Impala has 125k miles on it and drives just the same as it did with 50k miles. Don't allow the Honda boys on here to tell you that's the most reliable car on the planet. I've had cars that weighed more than a thousand pounds than a Civic, had twice the litre's and pistons, and beat them in gas mileage.
Every car has a lemon factor. Your best bet is to take someone who knows a lot about cars when you go shopping for a car. It will save you months and years of money pit issues.
Mazda's 929's and 626's are fairly reliable and their in abundance. You can find these car all over the place for less than you'd think. They are fairly nice looking cars that came with plenty of interior options. Take your time and don't buy the first thing that comes down the tube. And in my personal opinion, don't buy a Cavalier. Just because there's a shit ton of parts out for it doesn't make it any easier to fix. The same goes for a Civic.