In a race, nothing is more important that the position after the race. Of course, you do know that you need to be at your best to get at least the third spot. These three spots is where the big money is. Other position won't do at all.
Drive your car as fast as you can till you finish the race. Grab some coins that will be useful for upgrades. Hit any objects in the race as that add some points to your score later. But, the most important thing here is to finish the race no matter what position you got. At least, during your earlier tries, you can't expect to grab the top three spots, but that is just part of the game as you will have a better chance once you are fully upgraded.