Drift
For drifting, not only should you scrutinize what tire you are running, you should also take into account how much power you are making. Since the purpose is to control a car once your tires have broken loose, the stiffness of you springs and shocks should work in relation to this. Basic rule of thumb is, no power, low grip tires, go with stiff suspension. Big power, high grip tires, work better, to a point, with a softer setup. Many companies now make suspension geared specifically towards drifting. This means a suspension setup that allows for more understeer, as most drifters prefer. Whereas in road race, drivers prefer a neutral car or a car with a bit of oversteer. Keep in mind that when drifting you want the rear tires to break lose. Just as important will be how much you invest in adjustment arms. The lateral forces are so great going sideways, weak and worn out arms snap like twigs. Furthermore, there usually isn't adjustment for you to get enough steering angle, caster and camber. The further your skills progress, the further you'll need to invest in these arms.e.
Autocross/Road Race
This is probably the type of driving that will benefit the most from suspension tuning. But with so many different approaches to how a car should handle and so many variables, it can get overwhelming. The level of investment comes down to how much flexibility in adjustment and at what level you demand out of your car. It is quite intimidating when you see teams with $5-10,000 coilovers. But if you are not planning on competing at an unlimited class level (ie. dedicated racecar), it might be a little excessive.
If you are just enjoying the track on the weekends, you can definitely get away with a set of quality coilovers, upgraded sway bars and adjustment arms. Since many times, tires are limited by class, you can get a general idea of how stiff to set your suspension. Again start with a quality tire based on your needs. As you learn to understand your car more and more and drive it at full potential, you can start to adjust from there. Chassis stiffening, spring rates, sway bars, can all be adjusted to get the car to react in a way that is best suited to your driving style and ability.
Suspension shouldn't be approached as a per part perspective but as how the parts work as a whole. Tires, how much power you are making, and how you want your car to react, will all play a role in deciding how much adjustability you will need and what parts to invest in. Being able to properly understand what your needs are can reduce the amount of money wasted and get your car handling properly as well.