First of all make sure the car is in good condition. Cambelt, boost hoses, radiator and coolant pipes, and brakes will all take a hammering so make sure they are in good condition.
Next take some basic spares. At the very least a basic toolkit and some brake pads.
Other suggested spares are hose clips, fanbelt, fuel, water, duct tape and whatever else commonly falls off of your car!
Ditch all the weight you can as this is free performance. So take a full fuel can and a 1/4 full tank of fuel. Remove all the tools/spares/sparewheel and leave them trackside when you are racing. If you are feeling adventurous ditch the seats/interior too as the seats weigh quite a lot.
Your tyres are going to take a hammering too so if near the wear limits then you may want to take a set of spares, or a pair of fronts as these will take the most punishment.
Remember that on track your car will be pushed much harder than it ever will on the road so it WILL show up any weakness so be prepared to get towed home! Also incase the unthinkable happens you may wish to invest in trackday insurance as almost all normal car policies will exclude trackday use on it.
Lastly have fun. Take it easy to start with and keep it rubber side down.