Something not mentioned in the other 2 solutions, you DO NOT
have to buy the top/left skill on the box - it's the one with the number at the bottom of the tile - this is to do with getting boosts for a number of races, so it'll clear out & go grey again, so it doesn't count as a skill.
I got this by driving a car that I was having tons
of fun driving, and that's the Barn Find Mini with the power up as high as possible, drift suspension & Horizon tires - it drifts fabulously on roads, is small enough that you don't clip most things, and when 4WD it can pull easily on long drifts - I didn't get most of the skills using Demon Fox's solution of the beach, instead I was just driving around the countryside, finding Boards, Barn Finds and roads.
When fully upgraded it has over 500bhp, has a top speed of over 160mp/h, and is very light, so a lot of Danger Signs (and speed cameras) can easily be done with this car too.
Note that I wouldn't dare drive a Mini with this spec in real life - I would be pooping my pants the whole time.