I would wait until you have finished the game so you have a lot of good upgrades. Choose the Aurora (long thin craft). This is clearly the fastest class. Apply all the upgrades that give you the maximum speed attribute.
Mine were:
Engine - AUR M107
Hull - AUR Ultra Light
Wings - AUR A0M3
Now choose quick race:
League - Exhibition (doesn't matter)
Event - Velocity
Location - Paradise Isle
Course - Havoc
Condition - Clear (doesn't matter)
Choosing velocity is important because you want to get a couple of rockets attached and boost down the back straight (after the caves). There are multiple chances to get even more rockets. Don't worry about making the corner at the end, just keep boosting. You should get this 1st time round using the above settings.
Good luck and let me know if you need more help.