Game is rather difficult it will usually take few or more tries to win event.
My choice of cars for best results was:
Dorean LE (Time Attack Race class)
Hurricana CX (Time Attack Super class)
Motega XR/Ashburn '72 (Time Attack Street class)
If you want better cars faster I created few custom cities for XP grind, search by my gamertag. 25 min game on them will give you around 200-250k XP, over 100 targets destroyed and 130 prizes in one race.
EDIT: perceptron3000 gave few nice tips for 2 hardest tracks in comments.