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.
Drifting can be difficult when just starting. The first tip I can give is to buy a car that is drifting certified. It will have a sticker when your looking for a car to buy. A drifting car is built a little different and will drift easier than a non-drift car. I believe with the right tuning you can get a non-drift car to become a nice drift car but its cheaper to just buy a drift car to start with for now.
After a little practice you will get those 15,000 drift points. Take it slow and dont crash while in a drift or you will lose points you gained. Obtaining 15,000 drift points will seem very easy to do especially when you get to the level were you need to obtain 1,000,000 drift points.