No Rain Please!
The most basic thing to remember is that in the rain, although you are piloting the same car, the conditions will mean that you can often exceed the limits of grip even when accelerating in a relatively straight line. For those of us with street cars this is a big change, in a sense it is like adding 150 hp to your ride. Sliding the car in corners, without having induced it with power over steer, can also be accomplished at most any speed. The good news is that with the appropriate amount of caution this is a great learning opportunity. Rain can allow you to safely experiment with the unique handling characteristics of your car at a more relaxed pace. It gives your eyes and brain greater time to anticipate and react. You'll likely find that most instructors value the experience to some degree.
A set of rain tires is all that most drivers need to do to prepare their car. The suspension that I have is a street/track compromise. Typically my pace on a wet track is not affected as much as many of the others in my run group that have more dedicated track cars. The reason is that the softer more compliant set up that most of us has, while not ideal for dry conditions, is pretty well suited to the wet. If this describes your car it probably doesn't have a lot of negative camber either, and again in the wet that is to your advantage. At modest speeds it allows you to put a fat contact patch on the road and not exceed the tires grip. However, if you have a really great dry set up, or are looking at a lot of rain, you may consider going to the trouble of equally softening both of your sway bars. Some high-end suspensions even have adjustable shocks that offer the ability to easily change dampening settings in the pits. All of this techno-setup stuff is great but keeping it simple and just learning how to drive what you have is likely to offer more enjoyment, and greater benefit to your driving skills. All setups are a compromise.
After two or three years of track time most enthusiasts will want to invest in two wheel sets so that they have both dry and wet specific tires. If done correctly this allows you to effectively change set-ups just by changing your wheels. My car's suspension and alignment are biased to dry conditions. Most often I run Michelin Pilot Sport Cups on 18 inch BBS wheels in these sizes: 235/40-18 & 285/30-18. In the wet I use my stock 17 inch 993 rims with Bridgestone S03 in sizes: 205/50-17 & 255/40-17. Although it is not the ideal way to do this, I am effectively changing my car's suspension with the changes I make to the tires width and sidewall. The taller sidewalls of the tires are much more compliant and this simple tactic acts to soften the overall spring rate of the suspension. The tread pattern and narrow overall width of the tires slice through water and reduce the possibility of hydroplaning. The narrow width also means that I still achieve a full contact patch under the reduced cornering forces that generate less roll. These two tires have nearly identical overall diameters so the gearing of the car doesn't change.