Forget everything you know about fast cars for around twenty large. This is what you need to know: C5 Corvette Z06. Everything else is slow. The Mercury Grand Marquis sleeper with a turbocharger bigger than a 6 month old baby will be slower 99% of the time, and the slammed Toyota MR2 on racing slicks will not turn as well. For less than $20k you cannot get a faster overall vehicle than a C5 Z06. Find this 2003 Chevrolet Corvette Z06 offered here on eBay for $21,900 buy-it-now or make-offer, located in Jacksonville, FL.
The 2001-2003 Corvette Z06 took the already capable C5 chassis and turned the volume up to 11. It was also sold in decent quantity (28,388 during the 2001-2004 model years) due to its reasonable optional price and fantastic performance results. Want to get to 60 mph in 3.9 seconds and through the 1/4 mile in 11.97 seconds on the way to a 170 mph top speed? Add a skid pad rating of 1.03 G suddenly things get fast everywhere. No other unmodified factory vehicle will do this for about $20k and still be a decent daily driver.
The C4 Z06 is powered by the LS6 V8 (which is in essence a heavily modified version of the LS1) that puts out 405 horsepower (more like 425 horsepower according to owner dyno tests) and 400 ft-lbs of torque. Torque is abundant and these engines are known to go for 100s of thousands of miles on basic maintenance.
A 6-speed manual gearbox was the only transmission available in the C5 Z06 and its direct action will help you ignore the hard plastics and aging leather of the average C5 interior. If you get into the C5 expecting alcantara and Audi-esq build quality, you will be disappointed, but if your baseline is a 1993 Lumina, you will be thrilled!