For oversteering and stabilazation you will need to adjust the LSD controller, I have the same Skyline as you but I dont wanna tell you my exact setting becuase it differs with each driving style.
You will need to read about the LSD Initial Torque, the LSD Acceleration and LSD Deaceleration.
Each of them plays an important part in the car's stability and they can also affect your speed.
For example:
The LSD Acceleration determins the amount of power propelling the car when exiting turns.
if you set it too high, the car will get too powerfull and therefore oversteer and slide around.
You need to find the balanced point between the front and rear, becuase your car is powerful its recommended to set the rear to about 20-25 and the front to 45-50.
You also should set the spring rate to higher levels if you want your car to turn in a stabilized way, raising the spring rates means that you are increasing the pressure which is being applied on your tyres, and that will make your car more stable and controlable.
Also get Sports Breaks, Break Balance Controller, ASM, TCS and VCD System.
Strengthening the TCS will mean that your car will be more stable when turning but it will cost you in acceleration, but if you have a powerful car that shouldnt be a problem, so feel free to set it to about 6-7.
Break Stabilizers can be set to about 18-20.
Also for the oversteer, change the Stabilizer in the suspension costumization to a level which fits you most.
You will need to find the Angel of the Camber which fits you most and also the TOE.
Rideheight is also important, set it to a low level for maximum control, but not the lowest, 88-90 is enough
After youve completed all of these purchases and mods get Super Soft Racing Tires.
Test Drive your car, you will notice its gonna be easier to drive and you will have much more control.
If You still feel that the car is oversteering a bit, you will need to suit the suspension and breaks to the levels which suite you.
Hope I Helped.
P.S
Once Youve bought all the Engine modifications and equipped your car with a Turbo 4, you will have 1070HP and the widest gearing level should get you to about 392 kmph.
At least thats what I got.