I recently went car shopping with a friend with a $5,000 budget looking for the sportiest, best looking car we could find, and the 1991 Normally Aspirated (Non-Turbo) Toyota MR2 won hands down. MR2 stands for Mid-engined, Rear wheel drive 2 seater.
The MR2 is a pure sports car. Although the Normally Aspirated engine only outputs 130 horsepower, it outruns my 192 hp V6 Camry. This car uses a 4 speed automatic transmission, although a 5 speed manual is the transmission of choice.
The real shine of the MR2 is in it's handling. With the engine in the middle and the stiff suspension, it takes a real effort to lose grip on a corner. The ride is not bad, but you definitely feel the bumps in the road (which I personally prefer to a too-cushy luxury car ride).
Being a mid-engined two-seater, the insurance on an MR2 is higher than other cars from the price range. The lack of a back seat is not a big hassle as long as you don't have to transport more than one passenger. The hood of the car contains the spare tire and battery, and there is a rear trunk that may possibly hold a golf bag, and that's about it. There are storage areas behind the seats, with little containers on the floorboard, one of which has a lock. The seats are very comfortable and there is a surprising amount of leg room.
If your budget and taste is anything like my friend's, I would definitely recommend a Toyota MR2.