The stock WRX and STI suspension -- especially on older cars -- is biased more toward comfort and everyday use than all-out handling. We think the handling can be improved greatly without sacrificing too much ride comfort.
Pre-2015 WRX models have a suspension that is both soft and very tall, so body roll, squat (under acceleration) and dive (under braking) is the standard behavior. Lowering the car with either lowering springs or coilovers will lower the car's roll center, reducing roll, squat, and dive. Upgrading to aftermarket shocks will improve control of the suspension motion. Even the 2015+ cars can be improved with some careful adjustments, especially when it comes to the tall factory ride height.
In addition to springs and shocks, there are other suspension components that can be improved as well, including sway bars and suspension bushings.
Frame stiffening parts like strut tower bars help improve the rigidity of the chassis, which is especially helpful on the older cars.
Upgrading wheels and tires serves two purposes. Larger tires give increased grip and improved steering feedback. Bigger wheels provide more room for larger brakes.
Follow the links below for more detailed information on each subject.