Don't listen to these noobs, they are complete somewhere else talking ****... Ok, you want parts... stay at low level, don't get near lvl40 for a while and do races, West Park & Lyons /Rosewood & Lyons / Verona Tunnel and so on. Have the patience to do, try doing private races with your friends. You find something out

I don't know what's the actual part drop from races, keepin' in mind that this is a greedy game I think a pro/ultra part per 50-60 races :/
Secondly you have Treasure Hunt, waste of time, but using GMZ's hack for TH you can win lots of parts.
And at last Team Escape, boring... waste of time, try High Stakes, got a few parts there with a better drop.
If this didn't help you out then mate buy some ******* boost.