This organisation requires some changes from you. The changes below should provide you with everything you need for the Super Promotion.
Grip - If you're still using Nissan, you probably have all the maximum upgrades for him by now, and there's nothing much you can improve - time for a change. My choice is Mitsubishi Evolution (X not IX!). It's fast, but not as stable as Nissan, so if you're going to race on a really curvy road, switch back to your old chum.
Drag - Time for maximum tuning of your Charger if you haven't performed it before. Also, be sure to check the car settings and set them to optimal values.
Drift - If you picked Corolla, you might want to stick with it, as it should win you most (if not all) of the races. Buying a new car is not worth it, you just need to get a "feel" of your car.
Time Attack - Use Viper, BMW or buy something else. This race mode is all about skill and control, so the car choice is up to you, but be sure to tune it as much as you can.
If you can afford it, or you won a free car coupon you might consider picking up one of the higher class cars, such as Porsche.
Back to pre set cars. It's all about skill here, and if you're having problems in King mode, maybe it's not worth the effort?
Time Attack: A-54 Express Way
You can really speed up here, but be careful on the turns. Burn nitrous on the starting runway.
Grip: A-54 Loop
Another known track - you have to drive perfectly through the first part of the course, and then push it in the tunnels.
Drift: Drift Track B
Kiper drives a whole lot different than
Time Attack: Autobahnring C
Pay attention to staying on the road and don't worry about the U-turns, they only seem grim. Since all of your opponents ride the same cars, you might expect a crowd near the starting line.
Top Speed Run: Autobahnring A
If you're not sure which car to choose spend some time and test both. Track's not too difficult, but remember to burn nitrous near the checkpoints.
Drift: Drift Track D
Finally, a real challenge. In the first long bend you have to limit yourself to subtle drifts, then just keep switching from right to left, and if you enter the last turn properly, you might be able to keep drifting right up to the finish line.
If you liked the Viper, you might just pick it and use it for Top Speed Run. Skyline GT-R seems a poorer choice to me, but the decision's up to you.