Handling determines how fast and tidy of a racing line you can perform in a drift corner; also preventing your back end scraping on the edge of a corner. It seems that MR cars have the highest base handling stats. Because of the increased number of long drift corners later on in the story, having high handling is important in battles against difficult opponents. If you're using a FR car, make sure to increase handling as much as possible.
Tires can be acquired from the Daily Tire Event; you can only acquire up to Grade 11 from the Extreme category.
Parts are obtained from Story rewards, CP Orders, Gold Orders and Order Tickets. It is also possible to obtain these parts from the 24 Hour Part Races.