Just a little tip for the higher-level championships:
The best racers in each championship will often be racing cars that you haven't unlocked yet, especially if you are entering them as soon as they became available. So, to compensate, buy the best car you can from the specified manufacturer and try to match(or come close to, at least) the top speed and acceleration of the best car in the race using upgrades, otherwise you will get overtaken on the straights. Don't forget to balance this with handling upgrades as well.
You'll want your car to have a higher PI, obviously, but don't go too far; don't make the car harder to drive than it needs to be.
Hopefully your car won't turn out a complete disaster, and you'll be able to stay in front of the pack