I have a Subaru track car, while not a Skyline, the principles will hold the same.
The things that you should do are;
Safety - Put a cage in it, proper race seat and harness
Reliability - You don't want to build a car that can't cope with the extra stress involved.
Brakes - Get the best that you can afford, improve the brakes before you put extra power into the car
Weight - You don't need the interior, rear seats, boot lining etc, strip it out, save weight and gain braking and engine performance.
Tyres - R-specs minimum.
Suspension - Get coilovers if you can afford them, as well as getting parts that have enough adjustability as you can, so look at things like strut tops, adjustable sway bars, etc.
Power - Do this last, aim for the widest torque band that you can as that will help the car more than a "peaky" power curve.