In your career try going into your garage and upgrading (the little wrench) your car to its maximum for the rookie league. What this means to you: For each upgrade (power, weight, and handling) you need to complete a specific requirement (I can't remeber the rookie ones) and a 1 lap race against racer X. Don't upgrade until you are able to put on the max stuff because its a waste of money. Also, make sure the car you choose is a good drift car (there is a circle on the far right that says drift).
Same goes for your online career. I wouldn't worry to much about "finding matches" online, you can get all the way to the elite league and only race the AI characters. Select a goal card, select a race from the list and press the X button, select a car to use, wait the 9 or so seconds, and then race. The only races that require real people are the Team races, Pink slip races, and Twin drift races (some Twin drifts are also Pink slips).
Disclaimer:
This information is from memory so it may not be 100% accurate.
Good luck anyhow.
I don't drive faster than I can see.