Autocross courses are extremely compact. Since there aren't any long straightaways, having a lot of horsepower won't help you improve your lap times all that much. If you want to modify your car to deliver the fastest autocross lap times possible, focus on your car's suspension setup rather than performing engine modifications.
Performance Lowering Springs
You want to get your car's center of gravity as close to the ground as possible to reduce body roll. A set of performance lowering springs will drop the body of your car down closer to the wheels and axles, which will make your car corner much more flatly. Performance springs also have higher spring rates than your stock units. That means it takes more weight to compress them — in other words, they're much stiffer than your factory springs. When you're navigating tight corners around an autocross course, performance springs won't compress as much as your stock springs, which further reduces body roll and excessive weight transfer.
You need a set of performance shocks to complement your lowering springs. Your stock shocks aren't stiff enough to properly dampen the motion of performance springs with an increased spring rate. Installing performance springs on your stock shocks will make your car bounce excessively when you come out of corners or drive over uneven pavement. Furthermore, the shorter coils of your lowering springs will keep your stock shocks slightly compressed at all times, which will cause them to wear out prematurely.
With a set of performance springs and shocks installed, your car will corner much more flatly and predictably. Your stiffer suspension will also increase road feedback — you'll be able to feel your tires against the pavement. That makes it easier to feel the exact moment that your tires start to lose grip so that you can counter-steer and prevent your car from spinning out.
Increasing Negative Camber for Maximum Grip
When it comes to maximizing your car's handling potential, your wheel alignment is just as important as your suspension setup. Tuning your wheels with a bit of negative camber gives you more grip than having your wheels aligned flush with your suspension. When you go around a corner, the inertia of your car is constantly pushing against your tires in the opposite direction that you're turning. If you go too fast, the weight of your car overcomes the grip of your tires and you start to slide.
Negative camber essentially allows your tires to brace themselves against the asphalt and transfer some of the lateral force into the tire sidewall. Imagine you're playing tug-of-war — when you pull on the rope, you angle your feet toward the direction that you're pulling so that your shoes can dig into the ground and give you more leverage. Negative camber allows your tires to do the same thing while cornering.
Aftermarket Camber Kits
Lowering springs will throw the camber angle of your wheels out of whack because the wheels will be sitting at a different angle relative to the lowered body. Stock alignment components often don't have a wide enough range of camber settings to compensate for a lowered suspension setup. However, aftermarket camber kits give you a larger range of camber settings to choose from so you can get your wheels properly realigned.
Install an aftermarket camber kit along with your performance springs and shocks. Drive your car for a few days to give the springs a chance to settle completely. Then, take your car to a performance alignment shop and tell the technicians you want to set your car up for autocross racing. They'll tune your alignment settings with a bit more negative camber than your car came with from the factory in order to give your tires maximum grip.
A quality aftermarket suspension setup and a performance wheel alignment will allow your car to deliver drastically improved lap times around the autocross course. You can read more on this topic by following the link in this sentence.