Forget turbochargers, nitrous oxide, suspension kits, and all other go-fast goodies. The two best and cheapest ways to make your car quicker are a set of super-sticky tires and a serious upgrade of the organic software (that being you, the driver).
It Don't Mean a Thing If You Ain't Got Good Tires
Depending on whether you'll be driving on a twisty road-racing circuit or Decker Canyon, a set of sticky tires can be worth 50, 100, or even more horsepower. Slippery tires won't allow a car to translate its power advantage into cornering force and acceleration.
Here's a real-world example: Several years ago when I was organizing an event to give Michelin employees some seriously fast rides around a test track, I fit a 2001 Mustang GT with tires intended for a Dodge Viper and made the Ford nearly 3 seconds a lap faster around a 1.1-mile road course than a 1999 Porsche 911 shod with new, original-equipment tires.
The 911 enjoyed an advantage of roughly 40 hp. Its suspension was far more sophisticated than the Mustang's—a car that could trace its lineage directly to the 1978 Ford Fairmont. Both vehicles were stock except for roll cages and six-point racing seat belts, and the drivers were each professional tire testers and race drivers. (The Porsche driver, a Frenchman, was usually a bit quicker than me in the Porsche, and I was always better than he in the Mustang.) Yet your humble narrator beat him around the track.
If you want to go quicker in the corners, fit top-flight tires before you waste money on engine and suspension modifications.
My secret to beating the Porsche in the Mustang? The 275/35ZR18s intended for the front of a Viper boasted a tread compound that was nearly identical to a full-on race rubber. While the man in the Porsche drove his ego off, I just cruised around relishing the advantage.
Finally, my competitor employed two techniques that evened out the times: He jumped the curbs as one would on a racetrack (but was prohibited by Michelin internal regulations), and he refused to give rides to males, meaning I was carrying considerably more weight.
Speed Costs Money
A tire company spends about $1 million to develop rubber for a car like the Viper. The result will have unimaginable grip, slice through standing water, and give the driver ample warning they're approaching their limit of adhesion.
The upshot: If you're looking for replacement rubber for a vehicle built for performance, then the best max-performance tires will be the ones that came on your car. (Seriously, you spent six figures on the car and you're trying to save a few hundred dollars by putting on another brand?)
That said, sticking with original equipment tires won't fulfill your needs if those tires weren't meant for the high performance you're after. The Porsche would've smoked me if I'd fitted the Mustang with its original Goodyears. But I was willing to give up just about everything to make that old Fox-body Mustang kick some Stuttgart booty.
Two things I surrendered were turning radius and tire life. Those huge Viper fronts would've made parallel parking impossible. Not all upgrades are so impractical for the real world, but remember that you're going to sacrifice something in the pursuit of performance.
Know Your Jargon
Allow me to start what not to do in your search for stickier tires with this: Stay far, far away from all-season tires, even "ultra-high-performance all-season tires." All-season tires give up dry- and damp-road grip for traction at below-freezing temperatures. Look for a "summer" or, more accurately, a "three-season" tire.
The term ultra high performance once indicated tires that offered the highest grip. No longer. Now some sellers have created terms for tires that have far more traction than the old UHP nomenclature. "Max performance summer" is a step up, and often a big leap above, those labeled UHP. Tires that are even stickier are sometimes called extreme performance summer.