Try and buy the Ferrari F50GT! It has amazing speed and you can bring the back out around corners. Do not use the McLaren F1 as it has very good grip on the track and wont pick you up big points.
This is the method i use on the cone challanges:
Only go through the cones when you are not turning i.e going straight to pick up extra points.
When going round bends, Slow down to about 50mph and tap the E brake button, Once you do that hold the accelerate button and tap the E brake button again just to bring the back out a little further and remember to control the car so it does not spin out! Remember to power over and you will keep sliding!, Try not to hit the cones when sliding round the corner otherwise your powerslide will be wasted.
It is not important that you go through the cones on the corners as each cone you go through only gives you around 15 points. If you powerslide correctly around the corner and dont hit the cones round the bends, You should be picking up around 100-300 points on each turn.
Hope this helps in any way as its helped me to archieve GOLD in all the cone challenges in the game.