From my memory it was something like: Super Soft Tyres, Balance Frame Plus, Hi Torque V2.0, Gears i forget, High Cap Battery.
I race on the track to find a time to beat then i tend to spend time in the Test Track tweaking the setup until i'm close and then race again. If i win then i take the challenge. I have never needed to use boost to win a race so far. I'm on the last few races now and need to progress the story as parts get expensive quick!
I spent a few hours only doing races, substories and challenges and after a while you do get an idea of needs tweaking on the car and when a component is holding you back. Soft Tyre upgrades are the first i go for if i can afford them
You can buy parts in Don Quixote and there's a substory that gives you early access to some nice parts also.