I don't want to go in to detail, because I am not in front of my PS2, but basically you want to follow the 1000MPH escudo suspension tuning settings to do drag racing. Your transmission should just hit the fuel cutoff in 6th gear when you pass the finish line. For street racing, you need to analyze how you drive. (my big problem with th elicense tests)
If you drive SUPER agressive, bashing into walls, opponents and anything else you can find you need to make your suspension a lot more tolerant. You need to soften up the whole thing. it needs to roll with you and instant weight transfer is not required. (this is a valid, and VERY fast way to drive, but leaves you open for BIG errors that often cost you the race)
If you drive professionally, you need instant weight transfer, good brakes that match your drivetrain, and balance. These cars are like real race cars. They are stiff, nimble, but can spin like a scared cat if you arent careful. Ther is little room, for error, and you need to constantly maintain speed, or you are screwed.
There is a happy medium where most of us fall. Read the descriptions on the suspension parts in the settings menu to learn what they do.
The transmission is easy. For convenience, us the auto adjust to se it up. Run the course a couple times, and try to set it so that your speed governor/fuel cut off/rev limiter bounce at the end of the longest straightaway in the course. This will give you ample power to move really afast when you need to.