I do some "tracking" in Korea with the Tib. Even with performance springs it does alright. However, I would recommend a good set of coilovers (at least) if you are trying to push the envelope so to speak.
That being said, dmdicks' advice about maintenance is arguably the most important thing. Oil, transmission fluid (or gear oil), coolant, brake fluid, and power steering fluid (some just use ATF) should not be old or of poor quality. Take care of all leaks! From there, the next thing you will want to focus on is tires and brakes (brake pads at the very least). Edit: If I had to choose one thing to do first with limited funds, it would be brake fluid and brake pads. This will help the chances that you and your car make it through to the next track day, or at least the next upgrade opportunity.
Many people want to generate more power from the engine, but trust me, it won't help if the tires, suspension, and brakes can't put it to the ground consistently.
Oh and one more thing, you're also going to want to inspect any and all rubber bushings (especially the ones on the lower A-arms and engine roll-stoppers [some refer to them as front and rear engine mounts]).
Knowing the weaknesses of your car will help you understand how the car needs to be driven, and will help you be more efficient in upgrading both the parts of your car and developing the driving style that needs to be applied to your car's (current) configuration.